a-x-a-b-x-b-2-find-x-

Question Number 41032 by adityasin567@gmail.com last updated on 31/Jul/18

\frac{a}{x - a} + \frac{b}{x - b} = 2 . f i n d x .

Answered by tanmay.chaudhury50@gmail.com last updated on 31/Jul/18

a x - a b + b x - a b = 2 (x^{2} - a x - b x + a b)

2 x^{2} - 2 a x - 2 b x + 2 a b - a x - b x + 2 a b = 0

2 x^{2} - 3 a x - 3 b x + 4 a b = 0

2 x^{2} - 3 x (a + b) + 4 a b = 0

x = \frac{3 (a + b) \pm \sqrt{9 {(a + b)}^{2} - 4.2.4 a b}}{4}

= \frac{3 (a + b) \pm \sqrt{9 a^{2} + 18 a b + 9 b^{2} - 32 a b}}{4}

= \frac{3 (a + b) \pm \sqrt{9 a^{2} - 14 a b + 9 b^{2}}}{4}