Answer
$ \frac{1}{3x+5}$.
Work Step by Step
Add the numerators because denominators are same.
$\Rightarrow \frac{x^2-5x-2}{6x^2-11x-35}- \frac{x^2-7x+5}{6x^2-11x-35}=\frac{x^2-5x-2-(x^2-7x+5)}{6x^2-11x-35}$
Use the distributive property.
$\Rightarrow \frac{x^2-5x-2-x^2+7x-5}{6x^2-11x-35}$
Add like terms.
$\Rightarrow \frac{2x-7}{6x^2-11x-35}$
Factor $6x^2-11x-35$.
Rewrite the middle term $-11x$ as $-21x+10x$.
$\Rightarrow 6x^2-21x+10x-35$
Group the terms.
$\Rightarrow (6x^2-21x)+(10x-35)$
Factor each group.
$\Rightarrow 3x(2x-7)+5(2x-4)$
Factor out $(2x-7)$.
$\Rightarrow (2x-7)(3x+5)$
Back substitute into the fraction.
$\Rightarrow \frac{x^2-5x-2}{6x^2-11x-35}- \frac{x^2-7x+5}{6x^2-11x-35}=\frac{2x-7}{(2x-7)(3x+5)}$
Cancel common factors.
$\Rightarrow \frac{1}{3x+5}$.
