## Elementary Algebra

Published by Cengage Learning

# Chapter 7 - Algebraic Fractions - 7.1 - Simplifying Algebraic Fractions - Problem Set 7.1 - Page 281: 33

#### 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: $\frac{2n^{2}+5n-3}{n^{2}-9}$ =$\frac{2n^{2}-1n+6n-3}{n^{2}-3^{2}}$ =$\frac{n(2n-1)+3(2n-1)}{(n+3)(n-3)}$ =$\frac{(2n-1)(n+3)}{(n+3)(n-3)}$ =$\frac{(2n-1)}{(n-3)}$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.