Question

Solve for x: a/x-b + b/x-a = 2 By Factorization

Answer 1

The given equation is

$\frac{a}{x-b} +\frac{b}{x-a} =2$.

Multiply both sides of the equation by $(x-a)(x-b)$.

$(x-a)(x-b)(\frac{a}{x-b} +\frac{b}{x-a}) =2(x-a)(x-b)\\ a(x-a)+b(x-a) =2(x-a)(x-b)\\ a(x-a)+b(x-a) =2(x^2-(a+b)x+ab)\\ 2x^2-3(a+b)x+a^2+b^2+2ab=0\\ 2x^2-3(a+b)x+(a+b)^2=0\\ (2x-a-b)(x-a-b)=0\\ x=\frac{a+b}{2},a+b$

Thus the solutions are $x=\frac{a+b}{2},a+b$.

Answer 2

Answer:

We should FIRST multiply both the sides with (x-a) & (x-b)

Further steps are explained in the image..........

HOPE IT HELPS!!!!!!!!!