Answer
$$x=3,\:x=-5$$
Work Step by Step
Solving the equation by canceling out the denominators and simplifying, we obtain:
$$ \frac{15}{x}x\left(x+2\right)-\frac{15}{x+2}x\left(x+2\right)=2x\left(x+2\right)\\ 15\left(x+2\right)-15x=2x\left(x+2\right)\\ x=3,\:x=-5$$