Answer
$\frac{3x+2}{x-5}$.
Work Step by Step
The given expression is
$=\frac{6x^2+7x+2}{2x^2-9x-5}$
Factor $6x^2+7x+2$.
Rewrite the middle term $7x$ as $4x+3x$.
$=6x^2+4x+3x+2$
Group terms.
$=(6x^2+4x)+(3x+2)$
Factor each term.
$=2x(3x+2)+1(3x+2)$
Factor out $(3x+2)$.
$=(3x+2)(2x+1)$
Factor $2x^2-9x-5$.
Rewrite the middle term $-9x$ as $-10x+1x$.
$=2x^2-10x+1x-5$
Group terms.
$=(2x^2-10x)+(1x-5)$
Factor each term.
$=2x(x-5)+1(x-5)$
Factor out $(x-5)$.
$=(x-5)(2x+1)$
Substitute each factor into the given expression.
$=\frac{(3x+2)(2x+1)}{(x-5)(2x+1)}$
Cancel common terms.
$=\frac{3x+2}{x-5}$.
