Answer
$\frac{(2n-1)}{(n-3)}$
Work Step by Step
Since the numerator consists of a trinomial, we use the rules of factoring trinomials in order to factor it. For the case of the denominator, we use the rule $a^{2}-b^{2}=(a+b)(a-b)$ to factor it. Then, we cancel out the resultant common factors in the numerator and the denominator:
$\frac{2n^{2}+5n-3}{n^{2}-9}$
=$\frac{2n^{2}-1n+6n-3}{n^{2}-3^{2}}$
=$\frac{n(2n-1)+3(2n-1)}{(n+3)(n-3)}$
=$\frac{(2n-1)(n+3)}{(n+3)(n-3)}$
=$\frac{(2n-1)}{(n-3)}$
