Question

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Answer 1

Given to find the value of x:-

$\: \: \: \: \bf \: \dfrac{x - 1}{x + 2} + \dfrac{x - 3}{x - 2} = \dfrac{11}{8}$

SoLuTiOn :–

Taking L.C.M to the denominators.

$\: \tt \: \dfrac{(x - 1)(x - 2) + (x - 3)(x + 2)}{(x + 2)(x - 2)} = \dfrac{11}{8}$

$\tt \: \dfrac{x {}^{2} - 2x - x + 2 + x {}^{2} { + 2x} - 3x - 6}{x {}^{2} - 4 } = \dfrac{11}{8}$

$\tt \: \dfrac{2x {}^{2} - 4x - 4 }{x {}^{2} - 4 } = \dfrac{11}{8}$

By cross multiplication

$\tt \: (2x {}^{2} - 4x - 4)8 = 11(x {}^{2} - 4)$

$\tt \: 16x {}^{2} - 32x - 32 = 11x {}^{2} - 44$

$\tt \: 5x {}^{2} - 32x + 12 = 0$

Solving the Quadratic equation .

$\tt \: 5x {}^{2} - 30x - 2x+ 12 = 0$

$\tt \: 5x(x - 6) - 2(x - 6) = 0$

$\tt \: (x - 6)(5x - 2) = 0$

$\tt \: x = 6 \: and \: \dfrac{2}{5}$

So, tha value of x is 6 or 2/5