Answer
The solution is $x=-4$
Work Step by Step
$\bigg(\dfrac{x}{x+2}\bigg)^2=\dfrac{4x}{x+2}-4\hspace{0.7cm} \color{blue}{\text{Given equation}}$
$W^2=4W-4\hspace{3.3cm} \color{blue}{\text{Let } W=\dfrac{x}{x+2}}$
Or $W^2-4W+4=0$
$(W-2)^2=0\hspace{2.3cm} \color{blue}{\text{Factor}}$
$W-2=0\hspace{1.3cm} \color{blue}{\text{Zero-Product Property}}$
$W=2\hspace{1.99cm} \color{blue}{\text{Solve}}$
Now change $W$ back into the correspondimg values of $x$
$\dfrac{x}{x+2}=2$
$2x+4=x$
$-x=4$
$x=-4$
The solution is $x=-4$
