Question

solve for x

$\frac{x - a}{x - b} + \frac{x - b}{x - a} = \frac{a}{b} + \frac{b}{a}$
please give detailed solution
​

Answer 1

Answer:

$x = 0,a + b$

Step-by-step explanation:

$\frac{x- a}{x - b} + \frac{x - b}{x - a} = \frac{a}{b} + \frac{b}{a}$

$\frac{(x- a)^2 + (x - b)^2}{(x-a)(x - b)} = \frac{b^2 + a^2}{ab}$

$\frac{2x^2 -2(a+b)x + (a^2+b^2)}{x^2 - (a+b)x + ab} = \frac{b^2 + a^2}{ab}$

$2abx^2 -2ab(a+b)x + ab(a^2+b^2)= (b^2 + a^2)x^2 - (b^2 + a^2)(a+b)x + ab(b^2 + a^2)$

$2abx^2 -2ab(a+b)x = (b^2 + a^2)x^2 - (b^2 + a^2)(a+b)x$

$(b^2 + a^2)(a+b)x -2ab(a+b)x = (a - b)^2x^2$

$(a - b)^2(a+b)x = (a - b)^2x^2$

$x^2 - (a+b)x = 0$

$x(x - (a+b)) = 0$

$x = 0,a + b$