Answer
$ x=\dfrac{ab}{c}$
Work Step by Step
Multiply both sides by $(x-a)(x+a)$.
$(x-a)(x+a)\left (\dfrac{b+c}{x+a}\right )=(x-a)(x+a)\left ( \dfrac{b-c}{x-a} \right )$
Cancel common factors.
$\Rightarrow (x-a)(b+c) =(x+a)(b-c)$
Use FOIL method on both sides.
$bx+cx-ab-ac=bx-cx+ab-ac$
Add $ab+ac-bx+cx$ to both sides.
$bx+cx-ab-ac+ab+ac-bx+cx=bx-cx+ab-ac+ab+ac-bx+cx$
Simplify by combining like terms.
$2cx=2ab$
Divide both sides by $2c$.
$\dfrac{2cx}{2c}=\dfrac{2ab}{2c}$
Simplify.
$x=\dfrac{ab}{c}$
