Chapter 8 Quadratic Equations R.D. Sharma Solutions for Class 10th Math Exercise 8.3
Solve the following quadratic equations by factorization:
1. (x+4)(x+2) = 0
Solution
We have,
(x-4) (x+2) = 0
⇒ either (x-4) = 0 or (x+2) = 0
⇒ x = 4 or x = -2
Thus, x = 4 and x = -2 are two roots of the equation (x-4) (x+2) = 0
2. (2x+3)(3x-7) = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTNIJCmNyWADBcZByNeAKsGcg0oXaxRlWHut5T_8lSCsJSl_x0B7jEUMeuZhXyMxYBanxO9KVBNL6HkFdH5lhqh-CIPZPn-to6f2DhqCSwypjt-GPqgfNpKfS-tTegg6DQcXN0ZAhb1no/s400-rw/2+ans.PNG)
We have,
(x-4) (x+2) = 0
⇒ either (x-4) = 0 or (x+2) = 0
⇒ x = 4 or x = -2
Thus, x = 4 and x = -2 are two roots of the equation (x-4) (x+2) = 0
2. (2x+3)(3x-7) = 0
Solution
3. 3x2 – 14x – 5 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3pmLbTA5fREAjWtTPv0RQn7lJj5klL58lCEE8pl9aLX9x8XYcMtX-RhxCXmN0spD9SbuHKUdpmTsJz685rz1zbK6mOBwc0TtJJRvWV6VYym4NYZ7LpSYv9NqBP9wDOxgiz6y3wb9EtJY/s400-rw/3+ans.PNG)
4. 9x2-3x-2 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiafGI3NuHWC6fsjX1a32bG4uaXOynMBOshsmDOr8xLMpeS5ruUi5UDmdICMCCbSRiELXg5rQ3Jhqoy3BWsqlCnO25VEsieBhsPDoCQDTUj5D0DrzsFOIYcJgmBZ81SLLGuCC4yHeBCtRk/s400-rw/4+i.PNG)
5. 1/(x-1) - 1/(x+5) = 6/7, x≠1, -5
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjojuDOx8jbgd_E9LkMXrQT7WK5rvYG6-f9wA8DqDaymESqGF6zN9yyz6KUmXlH_Cz0vgtlwK-zIfskBbdhqVor1ELPgBr3P_iwJnUNoGlCtbG5b1dkInxBDlrKDMFCb8uL5Vm0hnTewXs/s400-rw/5+ans+%2527.PNG)
6. 6x2 + 11x + 3 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNo8bC4xB3bPrfrkMdYdF2nUzzUrO0TeUfL8fBOqugyPTLuyAfbE3HQLuNuttECrmF1Ewyh5FQnR3rrnElpZklG8h4rgH7SojeEyOMQhrRpz7BZywrQzVgOJXu53x8a129SDoBJQaq4YI/s400-rw/6+ans.PNG)
7. 5x2 – 3x – 2 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhyHnsIUow2GZK0GTv-J7HgM4jiOE6vMef4JK6CMWGQAzFFZtQZZU2Hl3mm8HNHNcNHmuZ2QCpmmTgK0KIgxIhCEmIhEg2ak0hO55WYlWGDoj_ybhdzdTzx5e0cYuyd8d63etKsD6SKF4/s400-rw/7+i.PNG)
8. 48x2 - 13x – 1= 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO_0s2KnFzJLDmRODUElJfAk7Sw05bDN1iUjBNoVcov4tpp7cX50WsF9PhcTcx4rZ9-owREFuTFL1bkoo9b4mbBJvOrpasHDO03z26c3eaGt6dh4QQJN4axcTVX5EnEZjmPtk4T426k2g/s400-rw/8+ans.PNG)
9. 3x2 = -11x – 10
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFT1xFJ98KJqQr441qP91r0EyaouSd9HqxYnN1I80AoSydn09LR7bygbYyCGa1sXiN9tyH2MNgAk-epVyVg1k6C7AIE8XuwxA_tnDpeIuqFPJPtnyLFoy5nwVeOnuOTvMT2sXCLEaegzM/s640-rw/9+ans.PNG)
10. 25x(x+1) = -4
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1j2SHxxSv1mroAvpwJcsQZyo95sgfpoVomr5rvYVFPak-qc9m6S2trTIWmS_cARk14rvS6uDTQzyYlpSu3OxhU9di9Cjb0xuigFWVWt7VN5oiXF6VSTIT6e6Fjue8YADQQme69m5QsLs/s640-rw/10+i.PNG)
11. 16x - 10/x = 27
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6xRsXtUvwtbpdOtbc3nosHBinWUjqgmuy7xCaojKqLRbcigNtHheQcY_KRa20BNgBzC-18VSdzbbIFcFVolpLzvpt5JwWllvE-9fcT4pQ4zrVuFCDoAbbZaqUjyB7_uDa2lVSukbcHrQ/s320-rw/11+ans.PNG)
12. 1/x - 1/(x-2) = 3, x ≠ 0, 2
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2IWPAIQbOcfiwNMfhb3uyB0CZ8boFDdfYF2fNI3x5WmRNw1le_jMeZ4pxipiFzx89pHl6A8N8mpC_EmrZLHMKxACU75xbDPTfiPjZU1bHaRZSgZPxQ_m_ghkRcAeGx6RubEmi65sILq4/s400-rw/12+i.PNG)
13. x - 1/x = 3, x ≠ 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiu88rbwZnwTQPp-MekLwEaThLkC3ncnf6QbF4Jp2_41af6Bc1PCrtD_pmriBZ4l61SD4PJS8euqjcQYCS5cJJOTlYXyAQyT3dUAma-HYmqlr_RuF_izepKjQEXO65A_88MRJYprlYUWL4/s640-rw/13+ans.PNG)
14. 1/(x+4) - 1/(x-7) = 11/30, x ≠ 4, 7
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO-7a0ZPgQYbGI1qybbasUF5vei3qGzDJaDZtTnvqTe-2Y4f_MjrA7xRZVK-j9pZFmzx9mpX8AZeF5dVDCz3qj26jS0Y2sW37JAP_j7BS7D7N5SS3_A8a6q3dGgX3B9pWuOIyoh_Kbl9M/s400-rw/14+i.PNG)
15. 1/(x-3) + 2/(x-2) = 8/x, x ≠ 0, 2, 3
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4R5tsG3HtqektfwQwSGINhMCKw4brirC4fDnYYYTBfgyM5wd3KQBky1rsG3C_SJiAUHmwLojAVULu2y-dfucPstg2Wc6Ut076uVx21qkZWhlJty179dY2YHG4hQd_YRgn1B6f5djOm04/s400-rw/15+i.PNG)
16. a2x2-3abx + 2b2 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhOLGDW4MMkjQW4I1ihqM5G556rZTSwfDumFlnS1qJE0YUvHFWAUpe5-HXTdvoLGffLYyELAl0nAZgRJd8_Y7EuGc6ODaRLFB-y3F4kVAfWAcUppoDOv4Gil1VLX4JCYI-inCmvZNWmpg/s400-rw/16+i.PNG)
17. 9x2 – 6b2x - (a4 - b4) = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIzxoDU6J5__lbEOspEFc4bhduOm0rmCBvSE3ebE2Mhisx-2vO2Cnl8ejLq5ISqHp5HCSQ7uzFgMuZ4WUBJ3lftCNbUcSI4qPqm1Aio_jXR-Q43LulxdD-co15-D2VgOIUzxXBUQoBRX0/s400-rw/17+ans.PNG)
18. 4x2 +4bx – (a2 – b2)
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOM6DEZOudnLJR9B5E-KY-ytwqlVc8BxP8AGGoCW5lEUbygqj-4TNRX6x3VLMPLzs1Yec98aUskS-33kVhy1dGaeC3GWvBX8TVsEfWNb6LjvjCxFabrXGGVNi3GdsjJjwg4GWpE4R3BF8/s640-rw/18+ans.PNG)
19. ax2 + (4a2 – 3b) x – 12ab = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkvm4gQvP229fX5WKTUjmpr-WpIePtdYRp3__Z0w1kgrPgIWIi0KvThG38ALmCEC5C-0aqdJvTnczpH1GXV8spfCqCDsaj9ln1dOdc5jIjccRH1RmQEltkl82TGTRhsI6mp0vCJgawP2U/s400-rw/19+i.PNG)
20 . 2x2 + ax - a2 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbY71h7UNFiizX7ASCxH3myo6DsT4UbAjhGlqDDZqLG5xxJ5aXFi1KWHrSBTyPe15sdMJ2457vVlrtoEUyHM_BYW7mFQN-lzKyQViGy-fUj0uARYCkcnVmo5v557uq-yrY9ZTuFfCorJg/s200-rw/20+ans.PNG)
21. 16/x - 1 = 15/(x+1), x≠ 0, -1
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_ct34ZFGOtefdwKKytf8puRsUxh5VI141F_0PL-NfmFGc2t5-SdW6OfKsO6Cdbl7TP2QHd5TO2iZMaeW2US5D97fjhAuf8Bz7GKs6VkDelPO8GFZQpTTDbx4-Og9BHXGjSRJ3ennkEN0/s320-rw/21+i.PNG)
22. (x+3)/(x+2) = (3x-7)/(2x-3), x ≠ 2, 3/2
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd-jVNtEPvdWqdOTgqrgRJhM2DHiY6dpbvzGOQnZS1eiljIZz6yX8fgBaOICI97EgcZ9eaBXhkKsgfLGMCPjrkI_3iccPoTcH_NOdNnbYV0LJjoEvy-LlT_tCcUl2WA_eFVvrhQdD_Khg/s400-rw/22+ans.PNG)
23. 2x/(x-4) + (2x-5)/(x-3) = 25/3, x ≠ 3, 4
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlO6tlw1N6ZqR28aXa0FE2phjYfv-19HN2q8wMcBHZadm8iKd3Nr3Ia-iYRwOaJXdbvJXS8G8Y7XZibfKxF6a01CFgirzcADgNWk3qLOEwOSOl1XbvCvx3d5iVZkzsTX7WU8oJmij-8is/s400-rw/23+i.PNG)
24. (x+3)/(x-2) - (1-x)/x = 17/4, x ≠ 0, 2
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2MK7jtFtckcGNqztxBbbw-IVoMQrsT3HxW1FkjR-KvqYZxLwJ74DXou4ObKwSXGkSQ4eEfaErstf2h2tNTWhZSIYhdeZ80f2-pW6eWa7h2wOb1_FCx9W-ZmYOxUDQZlezQEEZgOamp5I/s640-rw/24+i.PNG)
25. (x-3)/(x+3) - (x+3)/(x-3) = 48/7, x ≠ 3, x ≠ -3
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFQq5Xc5L4ALsWM7Zg3pQUon7X8qMMxxUFoFWcYg2rNTXz7QNRgYkV7AYDAvzzNO3Xor-bCDPjULyVHkI0l2sN_hbYcoeveqXfY5GcFc3Ds5hFIRi-b1MIg364dQZ9Kpq0UwHOEaImMTE/s400-rw/25+i.PNG)
26. 1/(x-2) + 2/(x-1) = 6/x, x ≠ 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipLD7wPh96yCQyO14AgbB6uzjejuoqn-Jx85Bm-nKuj4H4-F4-gABiomVBWAtezZ-2kpioe35ZfwwNxLFa73MoNTGumLyVKNLVyobOu4qI9gHIZO1fBh983BmzO6mab_6lHuwFxd9C4Ag/s400-rw/26+i.PNG)
27. (x+1)/(x-1) - (x-1)/(x+1) = 5/6, x ≠ 1, -1
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7rY94sBKJk80cLzYBlf8gqxFvmzALw7vBjJl4bvfWC21J2it_ZTe6_M5aFxVjMQ7AUk7UlMINTGug8f0QOJog0QumXpieEkGhrRrnBVRuPG1PUjJBeVaIrWIJGNV6u54Mv3NubVZraCY/s400-rw/27+i.PNG)
28. (x-1)/(2x+1) + (2x+1)/(x-1) = 5/2, x ≠ -1/2, 1
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7J1TNVhnJW8Umrzkw_H33cPfOcJ6QkWQepXKZai4840xMWGAa5nRKplM1soPxeMMmo1V45fS5LBrrxIai8A-C4VoV9Ej1Da_YPt448uA1XFProYT-3ZrrRQYUQr8dk_DWBpwkWFFXSN0/s400-rw/28+i.PNG)
29. 4/3 - 3 = 5/(2x+3), x ≠ 0, -3/2
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2HsABYXMArvSfgvIkJYTFOFqoUl4n7y-1mLbNSJAzBPQnOOXOB179t738ImuPuOZ1N0ab7mvJDTGwzRfJOVegWhjCcljNGH5P063l1zB-0TOLPG0EW4CTX5V-ltfr4B-UdkbwER3_vj4/s400-rw/29+i.PNG)
30. (x-4)/(x-5) + (x-6)/(x-7) = 10/3; x≠5, 7
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhznNGSR2AQ_5acIbps0xUC-SwG5q-rX2Tcc5_HCc9llQmm1VG2876NniCEtsLDno6qtItkWdmFndYq3V1voW1JWudXc7CmnSO7rYaI0LXiFe0vhj_XynxN91BaEbsQR28kqNnt0uOd_6k/s400-rw/30+i.PNG)
31. (x-2)/(x+3) + (x-4)/(x-5) = 10/3; x≠3,5
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqd5oDXPN_P-1E8Zb3wpzFY4KmapUi3aoMjnLNRDo3zlMCVbGNZFK1Q7xIpZVAkmY0qvC3NQTG0Z8JPPBFjD_Jai7gGJUnGJUp0PoNdGoDa5lz3TnH_fX_E3Tme6gq0Q3XAu6IQTWRmXI/s400-rw/31+i.PNG)
32. (5+x)/(5-x) - (5-x)/(5+x) = 3¾; x≠ 5, -5
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrt4pX1TUf2ffXr9jR_nieFKpYLCGe67FZAVc5Bv_JHJvgGAl7qOOvQyhtPtI4Yott8KlX0tz4Vwhk2eu6sOYJBhsxSsRRTG1qcqaeq_hFntJ0MebQj-FPOZfhQ5Pd7Dukr2-h2b8wRWU/s320-rw/32+i.PNG)
33. 3/(x+1) - 1/2 = 2/(3x-1), x≠-1, 1/3
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJpuTa0tZ_W20JP9ZoQt9OpNXWQ7cLqXYYEwSAi9fUM5ypc_j7bEn7wvzko1aGqwoEc_RAto879h8Lbeb9ap3l0n4FBCuEWlKqa4IQdhDEf0_16asSodpzRfcO6mNJHFdACUuufPMqWqw/s400-rw/33+i.PNG)
34. 3/(x+1) + 4/(x-1) = 29/(4x-1), x≠ 1, -1, 1/4
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEOhnEqwdg56tCyCwTB6Z74BLH0p00ievkQ2_wLbjYMEE5rVVguKVGJcGAxVU-HsAFbiBPdNrDTICmeoBas2LG7htIRrpfyMsbi-Q9WrL33ockr8tzX3P6DwgoBdrpDUS1qnKtvpKV-tQ/s400-rw/34+i.PNG)
35. 2/(x+1) + 3/2(x-2) = 23/5x, x≠ 0, -1, 2
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfJWWANBohFWnltD4v9-cxrEF1UEC7QCX3j1LZ2TIY7p0z-d4jJbyHIM1MK39ERI577GX7vR7_Cid1xvB2GJX50kOxHG60uaOG1nw_CmNlKau2Sfi4-_2UolDzmNBBhD-h2dl17pI8pvU/s400-rw/35+i.PNG)
36. x2 - (√3 +1) x + √3 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDnOu1pkpGwWKBD8MohPpw3VSLU1p4ZV-WQyvmTBHbSoFraSOfzfLrK_n78oBjD1IrGHazBgOSnaTss42dZsW97vSrRrF61jMOQz0W3bleLAf3OFVgt-6TsWCEU6-6lCsK14WPL2ahRa4/s200-rw/36+ans.PNG)
37. 3√5 x2 + 25x - 10 √5 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxIxRSBCqSUac6OGRYL2oKmMM5yFK8cUaOpOGEhhsnY4xOM8yeLTGKOt_SW3gbvWmxyhMTUpQyGIVcktgJiTr-DlWC528tMqBRXSeXaBmGbB0yu_LCyYkIQvMFclUIdCJ8Rk0iFNyzM5w/s320-rw/37+i.PNG)
38. √(3x2) - 2√2x - 2 √3 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiulQKqZ9IPmea27AhKOPqRW_drdeMfFLMH0aDWXFLvsqwC3HzdI-qf9-p4WpG38IrvcSk3hqlHqFSgWlNXuhbC_KMYYIX_QctcRCKu3nFucwk0AsqFBQIUMV0vD678w7yxNeo0INYhn9g/s320-rw/38+ans.PNG)
39. 4√3 x2 + 5x - 2 √3 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjc_T9u0_3BX5OMVRu1H8Kpmb7PQrVeRQH_vNjNs6p0THVuHVLRt4C68mLgiUDZUdBmDI4kGFrX6ZefrDFSCDgYsQ96PCcj-FoQs0sYyTS9w9lUbo3Bl901VmGUVuActw70Wm5S8IIrPY0/s400-rw/39+i.PNG)
40. √2 x2 - 3x - 2√2 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8AoQBGVornsWfj_Vq7LmW06K8CuHmV7wuyAPcvYeCxhVYOEtAszN6_u-OoVHju-qpJTODrxYYu19GufHujLFheAMbEkSXX33BL3z6hf68oASf7oSFm2ui8XYC7u7jMuE_yyKiLwexxEw/s400-rw/40+i.PNG)
41. x2 - (√2 + 1)x + √2 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiulOvdNpEDJDXKT1lhqvcDkcXL1_-C2zSppaReXrDu1rejozxzJhAe9S-cXzNL89_-edcaRt6UhBXHO2H-fSn_W-KIgQXnlEuGKvXnX129Jkp1khDP74Y8wVkyLlVDocWVdjOULKjgNCw/s200-rw/41+ans.PNG)
42. 3x2 - 2√6 x + 2 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAc2dIbQxriQ46mMvmflnNYXQDtuz6MZZ9snrgEV4HVkYZEl4b3ElESv76AboA9FzBvNL-49bOdoCgANmu0wP3RYY0SxleI6aUS-iOTpLj8_Dlmsy6Kq5Pp8gz2wSYPW1fpfBc8FaFD74/s400-rw/42+i.PNG)
43. x2 - 4√2 x + 6 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLQnHCVBm7v5ZZBdxgjIhKWAryFQIjvTeIeQhRPuFAqr3_gs6n12kvlio8KZQnO-h43Sbvwtiehgctc32YJiVEowcyKfSQc1So1m2G8gXeVUqbYaafaptGDK9ispnj-l_J62ncdzpi8Sk/s200-rw/43+ans.PNG)
44. m/n x2 + m/n = 1- 2x
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhluL47ZjjrnfnsfQXuM3-TYY6udKD7mKAWPAaPiKwYHdUfwAKzsdMIzKY1nNcLE_PMcPI1R-QVRKx4dmjq2gtwfbMiYRirCm2Dw_qvBEdZl_r7I7-7p02frwIZTBqqFBXvT50Nsqr-10o/s400-rw/44+i.PNG)
45. (x-a)/(x-b) + (x-b)/(x-a) = a/b + b/a
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnDC1fhdXtgX9ielVuUv50F-ZbT8lqOPBKFnKe8nnSkN-0OlDk3Nbv16TL6nLnYEU-JK1VmDuh7LeOMslMKjzQoyt9UScUc-ii8LIXqPTHuPqboubVDAdohbhzUCb4hR8pPXi0i5aHcss/s400-rw/31+i.PNG)
46. 1/(x-1)(x-2) + 1(x-2)(x-3) + 1/(x-3)(x-4) = 1/6
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnqhS_geHun7WBctc4eXv0KXqGSokj1EmIltpawmBNHOwirunwjJtCcXgUHM2qBLv-riKU_zFjkgtqm3mrQMyIVMrcMzowYYW9nIO1gO3hE9u6PS-fR1oH4qaADB3Lyusc4Se9SvXQB1E/s640-rw/46+i.PNG)
47. a/(x-b) - b/(x-a) = 2, x ≠ a,b
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-3VNWuZe-xaEl7sPf11HnwLadcmlFuX64dg3T-7f2BBHtjCdodzLr7Td5KfZko8OKTTYvVWjJCGJaeYDDxARYQtbrrkIymY5sDtELJGueYaNaSdhi0ZP58-zLEISLRHAIMXYn3DHAOAA/s400-rw/47+i.PNG)
48. (x+1)/(x-1) + (x-2)/(x+2) = 4 - (2x+3)/(x-2); x≠ 1,-2, 2
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUuRZCI5ASor3TYiqlDZL1wMXqmo3gXIPr9NUgvVLD6SXS-Vz4qwefD_oJcicHk45lAd7p8cNoFNLbWv317Q3nOLQeMDMP4Dch6m6fIuBKHo_IJC0Q-_Cer3MhV75ROD76ANfTVw8_1Jk/s400-rw/48+i.PNG)
49. a(x-a) + b/(x-b) = 2c/(x-c)
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4T6OLe_SK_VyxBIB6zkr7bFCVwT8rBtcWMu90lQrc78z1_D93-2Kj6230hPvAqyUE8W-KlH5iEtblpImB3IO8eh30cnz-rK1tgGib6smJJHcu7pq18Oe4Nb_b1BZcjsQiBOePsZ_0FDw/s640-rw/49+i.PNG)
50. x2 + 2ab = (2a+b)x
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhM7rwNyguXHZnN4yY7Kfzy54fOGmHQzlxBy5Meobl_xhASiYufcjd2vwCflSirDtlG-EcVF1mDOlAQlyJrZ5FClPmafb5j3Dog15lwIpMdC3RWGTZxstp918M0DntAujgBtOeNcM0SLdI/s400-rw/50+ans.PNG)
51. (a+b)x2 - 4abx - (a-b)2 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiplqGVTLM9Ht1UqtvYey5nOZzjmdpkFI-qwiOGMybhOFekDoUVYfIa6QrKNnv2flsOQy3I92-198dWNe19HLNT3gG2E7W1iORXUqILw9iKj7XFZ1VIcZIrttWMPJrJWLD1LXjIPpCywIo/s640-rw/21+ans.PNG)
52. a(x2+1) - x(a2+1) = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_P177nj3JKv6aKYj7y3w6U6ilkivRr1OcFSzYOazgwZkWiOhI3MzeMnZliftbp_VrJJVYdLzOsaloLLfEbO-MD83BQuwo2pLn1kw4XgqzNfBziRno3KZSmBrvZZUP4V7cVgpFRfdbmxQ/s400-rw/38+i.PNG)
53. x2 - x - a(a+1) = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYIfVmgaTFeLl3DBTQMOiPEoJBKRWO2aFC6v0vMpY-6dQ1DYyQpAHzFkXduRZ_CboGXDa4HLr7iXueJz1MF4MS4gaGsQWmCOxSmBUl1S2_k1gxkTP3jWn_U9rwly8LFN3WR4M8cduIsBY/s400-rw/53+ans.PNG)
54. x2 + (a+1/a)x + 1 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9dUmcqFsABXwA5f2d2F-b4co357IXSDdS6zsxpbubnhbTDjVD_EgBQbV8oPITpg6nr8BmTiyF5p0xn0rGP56eRsVp2jiBh7CCsWZd8FpCLfNpNBJiV6N0JHaGcqlI-TVMGLxYLal19EY/s320-rw/40+i.PNG)
55. abx2 + (b2-ac)x - bc = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbMdg7XVbxK1dOvPWRh08csaI5PWMZVq6Ras_7A0nO8jlm-CqSx2CMeuV-tJHLz53UpLL8TtqQYu7Nqc9uwXoPSd04Q3T5TWV1ZLvlihn9o47doZhBLh1-PMqAcNWGQ84RvhnecooRXuw/s400-rw/41+ans.PNG)
56. a2b2x2+ b2x - a2x -1 = 0
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0hIM-1QW735hbkviwaOWxOrHq0gy3zNR2DNT-tDrzejQe9wJnMQAu0JEV_MM9tMAxjmMpo9aD1PsL7ZA0L2N5cdP4of1BLeKtp3swbt_KkSDU6mBBAe675Edzv2MgvAQtfyKzGk94_78/s400-rw/57.PNG)
57. (x-1)/(x-2) + (x-3)/(x-4) = 3⅓; x≠ 2, 4
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjisg9ZRlGbD25_y3bOSXtO6Zrx59eH3POrhn43PmOKxLZXgVGw83OwOZTPhG-NxiTPdn7J6XKms_8ULwRh2oFHyxZtX-hCURLQHPRN3If71EhhCi9FI-3yDFehBH9-vJd-teHg4Ny9g38/s400-rw/57+i.PNG)
58. 1/(2a+b+2x) = 1/2a + 1/b + 1/2x
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7OOwg0U3NB2bK2JSAWkjU6ZeTPB8YBq7GMN7Oa6k6NEt3BpgMOlnYZTkLwhVnCs2wW39Taqtgiz9y175P47Chyphenhyphen8UE0p6HFvo3bEESyIEPVjKnJatxhgYLSh5hijdxl9r7Ongdh3FbQB4/s400-rw/58+i.PNG)
59. 3{(3x-1)/(2x+3) -2{(2x+3)/3x-1)} = 5; x≠ 1/3, -3/2
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiu04IMyuYNbsOj0NLT8hWvhZ9NZO6PXIjHqhNzDkd5eEChJLwPWNXpjRLEIdAojI8aobnJcVwBZWXgrKTx25ykaUCOrejwAr1DAVfZ-gDVwccPvhyV_PACg6Pd3kiwNU11Bi2UPQjoJyY/s320-rw/59+i.PNG)
60. 3{(7x-1)/(5x-3)} - 4{(5x-3)/(7x+1)} = 11; x≠ 3/5, -1/7
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1K-R53TKhzKHq7LO19vk9463-Q_x38tQt2MO4fNUnkdV9awYnk6ErcBAl9FaTD1ROL4ZD8T8-U2PJsgGSa0smKJ2XXKzQ-WacABMMbjzXZ0rJlAQ63xlOIhFBr-PXtkLxY56eXsFnTis/s400-rw/60+i.PNG)
61. (x-5) (x-6) = 25/(24)2
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLObg11Sk850wa42SVI5hb00dKQCVu1Z3DDZBgohhqLWdmwQrZI2nD4Th0e1i816gWZ7avb-S7pk0AGNq4SFSQSD5vwTOFrXtTwCtFRhUqGtr9rQ4P6XYU4G3XJ_kTE88zBgo-AeqWtEs/s400-rw/61+i.PNG)
63. 7x + 3/x = 35 3/5
Solution
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiMSne7oRu3C7CiC7RCCYWPosxxyulbZ_7yXwnkFFTML0R-2a4hrgn9V0ijG25UrVte0LapsU5kO1k7dO4oe2kP9K0U5eoPDcIyqxPG-8h5Xpqszj2MHeTp-g6C19wIC8FMUbu34YE4zQ/s400-rw/63+i.PNG)
Solution
4. 9x2-3x-2 = 0
Solution
5. 1/(x-1) - 1/(x+5) = 6/7, x≠1, -5
Solution
6. 6x2 + 11x + 3 = 0
Solution
7. 5x2 – 3x – 2 = 0
Solution
8. 48x2 - 13x – 1= 0
Solution
9. 3x2 = -11x – 10
Solution
10. 25x(x+1) = -4
Solution
11. 16x - 10/x = 27
Solution
12. 1/x - 1/(x-2) = 3, x ≠ 0, 2
Solution
13. x - 1/x = 3, x ≠ 0
Solution
14. 1/(x+4) - 1/(x-7) = 11/30, x ≠ 4, 7
Solution
15. 1/(x-3) + 2/(x-2) = 8/x, x ≠ 0, 2, 3
Solution
16. a2x2-3abx + 2b2 = 0
Solution
17. 9x2 – 6b2x - (a4 - b4) = 0
Solution
18. 4x2 +4bx – (a2 – b2)
Solution
19. ax2 + (4a2 – 3b) x – 12ab = 0
Solution
20 . 2x2 + ax - a2 = 0
Solution
21. 16/x - 1 = 15/(x+1), x≠ 0, -1
Solution
22. (x+3)/(x+2) = (3x-7)/(2x-3), x ≠ 2, 3/2
Solution
23. 2x/(x-4) + (2x-5)/(x-3) = 25/3, x ≠ 3, 4
Solution
24. (x+3)/(x-2) - (1-x)/x = 17/4, x ≠ 0, 2
Solution
25. (x-3)/(x+3) - (x+3)/(x-3) = 48/7, x ≠ 3, x ≠ -3
Solution
26. 1/(x-2) + 2/(x-1) = 6/x, x ≠ 0
Solution
27. (x+1)/(x-1) - (x-1)/(x+1) = 5/6, x ≠ 1, -1
Solution
28. (x-1)/(2x+1) + (2x+1)/(x-1) = 5/2, x ≠ -1/2, 1
Solution
29. 4/3 - 3 = 5/(2x+3), x ≠ 0, -3/2
Solution
30. (x-4)/(x-5) + (x-6)/(x-7) = 10/3; x≠5, 7
Solution
31. (x-2)/(x+3) + (x-4)/(x-5) = 10/3; x≠3,5
Solution
32. (5+x)/(5-x) - (5-x)/(5+x) = 3¾; x≠ 5, -5
Solution
33. 3/(x+1) - 1/2 = 2/(3x-1), x≠-1, 1/3
Solution
34. 3/(x+1) + 4/(x-1) = 29/(4x-1), x≠ 1, -1, 1/4
Solution
35. 2/(x+1) + 3/2(x-2) = 23/5x, x≠ 0, -1, 2
Solution
36. x2 - (√3 +1) x + √3 = 0
Solution
37. 3√5 x2 + 25x - 10 √5 = 0
Solution
38. √(3x2) - 2√2x - 2 √3 = 0
Solution
39. 4√3 x2 + 5x - 2 √3 = 0
Solution
40. √2 x2 - 3x - 2√2 = 0
Solution
41. x2 - (√2 + 1)x + √2 = 0
Solution
42. 3x2 - 2√6 x + 2 = 0
Solution
43. x2 - 4√2 x + 6 = 0
Solution
44. m/n x2 + m/n = 1- 2x
Solution
45. (x-a)/(x-b) + (x-b)/(x-a) = a/b + b/a
Solution
46. 1/(x-1)(x-2) + 1(x-2)(x-3) + 1/(x-3)(x-4) = 1/6
Solution
47. a/(x-b) - b/(x-a) = 2, x ≠ a,b
Solution
48. (x+1)/(x-1) + (x-2)/(x+2) = 4 - (2x+3)/(x-2); x≠ 1,-2, 2
Solution
49. a(x-a) + b/(x-b) = 2c/(x-c)
Solution
50. x2 + 2ab = (2a+b)x
Solution
51. (a+b)x2 - 4abx - (a-b)2 = 0
Solution
52. a(x2+1) - x(a2+1) = 0
Solution
53. x2 - x - a(a+1) = 0
Solution
54. x2 + (a+1/a)x + 1 = 0
Solution
55. abx2 + (b2-ac)x - bc = 0
Solution
56. a2b2x2+ b2x - a2x -1 = 0
Solution
57. (x-1)/(x-2) + (x-3)/(x-4) = 3⅓; x≠ 2, 4
Solution
58. 1/(2a+b+2x) = 1/2a + 1/b + 1/2x
Solution
59. 3{(3x-1)/(2x+3) -2{(2x+3)/3x-1)} = 5; x≠ 1/3, -3/2
Solution
60. 3{(7x-1)/(5x-3)} - 4{(5x-3)/(7x+1)} = 11; x≠ 3/5, -1/7
Solution
61. (x-5) (x-6) = 25/(24)2
Solution
63. 7x + 3/x = 35 3/5
Solution