smc

Use a common denominator: $\frac{15-2(x+2)}{x^2-4}=1$. After moving the $1$ to the left side, notice that you can factor the numerator: $$\frac{(x-5)(x+3)}{x^2-4}=0$$ The roots of this equation are $\boxed{-3\text{ and }5}.$