Answer
$=\displaystyle \frac{x+1}{x+2}$
Work Step by Step
The expression in the parentheses is a difference of rational expressions with equal denominators,
$\displaystyle \frac{3x-1}{x^{2}+5x-6}-\frac{2x-7}{x^{2}+5x-6}=\frac{3x-1-(2x-7)}{x^{2}+5x-6}$
$=\displaystyle \frac{x+6}{x^{2}+5x-6}$
... factor the denominator,
$=\displaystyle \frac{x+6}{(x+6)(x-1)}\qquad$ ... common factors cancel
$=\displaystyle \frac{1}{x-1}$
The problem now equals
$\displaystyle \frac{1}{x-1}\div\frac{x+2}{x^{2}-1}$
... dividing with $\displaystyle \frac{A}{B}$ equals multiplying with $\displaystyle \frac{B}{A}$
=$\displaystyle \frac{1}{x-1}\times\frac{x^{2}-1}{x+2}$
... recognize the difference of squares
$=\displaystyle \frac{(x+1)(x-1)}{(x-1)(x+2)}\qquad$ ... common factors cancel
$=\displaystyle \frac{x+1}{x+2}$
