Answer
The solution set is $\{\frac{3}{4}\}$.
Work Step by Step
The given equation is
$\frac{1}{x+2}+\frac{15}{x^2-4}=\frac{5}{x-2}$
Factor the denominator:
$\frac{1}{x+2}+\frac{15}{(x+2)(x-2)}=\frac{5}{x-2}$
Multiply the equation by $(x+2)(x-2)$
$\frac{(x+2)(x-2)}{x+2}+\frac{15(x+2)(x-2)}{(x+2)(x-2)}=\frac{5(x+2)(x-2)}{x-2}$
Simplify.
$(x-2)+15=5(x+2)$
$x-2+15=5x+10$
$-2+15-10=5x-x$
$15-12=4x$
$3=4x$
$\frac{3}{4}=x$.
