Answer
$-\frac{12}{5}$.
Work Step by Step
The given expression is
$=\frac{\frac{3}{x+2}-\frac{3}{x-2}}{\frac{5}{x^2-4}}$
Factor the term $x^2-4$
Use the algebraic identity $a^2-b^2=(a+b)(a-b)$.
$=x^2-2^2$
$=(x+2)(x-2)$
$=\frac{\frac{3}{x+2}-\frac{3}{x-2}}{\frac{5}{(x+2)(x-2)}}$
Multiply the numerator and the denominator by $(x+2)(x-2)$.
$=\frac{(x+2)(x-2)}{(x+2)(x-2)}\cdot \frac{\frac{3}{x+2}-\frac{3}{x-2}}{\frac{5}{(x+2)(x-2)}}$
Use the distributive property.
$=\frac{(x+2)(x-2) \cdot \frac{3}{x+2}-(x+2)(x-2) \cdot \frac{3}{x-2}}{(x+2)(x-2) \cdot\frac{5}{(x+2)(x-2)}}$
Simplify.
$=\frac{3(x-2) -3(x+2)}{5}$
$=\frac{3x-6 -3x-6}{5}$
$=\frac{-12}{5}$
$=-\frac{12}{5}$.
