Answer
$x=0$
Work Step by Step
$\dfrac{2}{x-2}+1=\dfrac{x}{x+2}$
Multiply the whole equation by $(x-2)(x+2)$ to eliminate all denominators:
$(x-2)(x+2)\Big(\dfrac{2}{x-2}+1=\dfrac{x}{x+2}\Big)$
$2(x+2)+(x-2)(x+2)=x(x-2)$
Evaluate the indicated operations:
$2x+4+x^{2}-4=x^{2}-2x$
Take all terms to the left side of the equation and simplify it by combining like terms:
$x^{2}-x^{2}+2x+2x+4-4=0$
$4x=0$
Solve for $x$:
$x=0$
