Answer
$x=a^2$
Work Step by Step
Multiply both sides by $(x-a)(x+a)(x-1)$.
$(x-a)(x+a)(x-1)\left ( \dfrac{1}{x-a} + \dfrac{1}{x+a}\right )=(x-a)(x+a)(x-1) \left (\dfrac{2}{x-1} \right )$
Use distributive property and cancel common factors.
$(x+a)(x-1) +(x-a)(x-1)=2(x-a)(x+a)$
Factor out $(x-1)$ on the left and use special formula $(a+b)(a-b)=a^2-b^2$ on the right.
$(x-1)(x+a +x-a)=2(x^2-a^2)$
Simplify.
$(x-1)(2x)=2x^2-2a^2$
$2x^2-2x=2x^2-2a^2$
Subtract $2x^2$ from both sides.
$2x^2-2x-2x^2=2x^2-2a^2-2x^2$
Simplify.
$-2x=-2a^2$
Divide both sides by $-2$.
$\dfrac{-2x}{-2}=\dfrac{-2a^2}{-2}$
Simplify.
$x=a^2$
