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1) 1/(x - 1)(x - 2) + 1/(x - 2)(x - 4) + 1/(x - 3)(x - 4) = 1/6 where, x not equal to 1,2,3,4.Please don't Spam |
Answer» EXPLANATION.⇒ 1/(X - 1)(x - 2) + 1/(x - 2)(x - 4) + 1/(x - 3)(x - 4) = 1/6. Taking L.C.M in this equation, we get. ⇒ (x - 3)(x - 4) + (x - 1)(x - 4) + (x - 1)(x - 2)/(x - 1)(x - 2)(x - 3)(x - 4) = 1/6. ⇒ (x - 3)(x - 4) + (x - 1)[(x - 4) + (x - 2)]/(x - 1)(x - 2)(x - 3)(x - 4) = 1/6. ⇒ (x - 3)(x - 4) + (x - 1)[x - 4 + x - 2]/(x - 1)(x - 2)(x - 3)(x - 4) = 1/6. ⇒ (x - 3)(x - 4) + (x - 1)(2x - 6)/(x - 1)(x - 2)(x - 3)(x - 4) = 1/6. ⇒ (x - 3)(x - 4) + (x - 1)2(x - 3)/(x - 1)(x - 2)(x - 3)(x - 4) = 1/6. ⇒ (x - 3)[(x - 4) + 2(x - 1)]/(x - 1)(x - 2)(x - 3)(x - 4) = 1/6. ⇒ (x - 3)[x - 4 + 2x - 2]/(x - 1)(x - 2)(x - 3)(x - 4) = 1/6. ⇒ (x - 3)(3X - 6)/(x - 1)(x - 2)(x - 3)(x - 4) = 1/6. ⇒ (x - 3)3(x - 2)/(x - 1)(x - 2)(x - 3)(x - 4) = 1/6. ⇒ 3/(x - 1)(x - 4) = 1/6. ⇒ (x - 1)(x - 4) = 18. ⇒ x² - 4x - x + 4 = 18. ⇒ x² - 5x + 4 = 18. ⇒ x² - 5x - 14 = 0. Factorizes the equation into middle term split, we get. ⇒ x² - 7x + 2x - 14 = 0. ⇒ x(x - 7) + 2( x - 7) = 0. ⇒ (x + 2)(x - 7) = 0. ⇒ x = -2 & x = 7. |
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