Answer
$\frac{5x-6}{(x-5)(x+3)}$.
Work Step by Step
The given expression is
$=\frac{7x}{x^2-2x-15}-\frac{2}{x-5}$
Factor $x^2-2x-15$.
Rewrite the middle term $-2x$ as $-5x+3x$.
$\Rightarrow x^2-5x+3x-15$
Group the terms.
$\Rightarrow (x^2-5x)+(3x-15)$
Factor each group.
$\Rightarrow x(x-5)+3(x-5)$
Factor out $(x-5)$.
$\Rightarrow (x-5)(x+3)$
Back substitute into the fraction.
$=\frac{7x}{(x-5)(x+3)}-\frac{2}{x-5}$
The LCD is $(x-5)(x+3)$.
Multiply the numerator and the denominator:
$=\frac{7x}{(x-5)(x+3)}-\frac{2(x+3)}{(x-5)(x+3)}$
$=\frac{7x-2(x+3)}{(x-5)(x+3)}$
Use the distributive property.
$=\frac{7x-2x-6}{(x-5)(x+3)}$
Simplify.
$=\frac{5x-6}{(x-5)(x+3)}$.
