Answer
$\frac{1}{x+3}$.
Work Step by Step
The given expression is
$=\frac{2x-7}{x^2-9}-\frac{x-4}{x^2-9}$
Add numerators because both denominators are the same.
$=\frac{2x-7-(x-4)}{x^2-9}$
Clear the parentheses.
$=\frac{2x-7-x+4}{x^2-9}$
Add like terms.
$=\frac{x-3}{x^2-9}$
Factor $x^2-9$.
$=x^2-3^2$
Use the algebraic identity $a^2-b^2=(a+b)(a-b)$
$=(x+3)(x-3)$
Substitute the factor into the fraction
$=\frac{x-3}{(x+3)(x-3)}$
Cancel common terms
$=\frac{1}{x+3}$.
