# Chapter 7 - Section 7.3 - Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator - Exercise Set - Page 509: 56

$\dfrac{12x-6}{x^{2}+3x}\cdot\dfrac{4x^{2}+13x+3}{4x^{2}-1}=\dfrac{6(4x+1)}{x(2x+1)}$

#### Work Step by Step

$\dfrac{12x-6}{x^{2}+3x}\cdot\dfrac{4x^{2}+13x+3}{4x^{2}-1}$ Factor both rational expressions completely: $\dfrac{12x-6}{x^{2}+3x}\cdot\dfrac{4x^{2}+13x+3}{4x^{2}-1}=\dfrac{6(2x-1)}{x(x+3)}\cdot\dfrac{(x+3)(4x+1)}{(2x-1)(2x+1)}=...$ Evaluate the product and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{6(2x-1)(x+3)(4x+1)}{x(x+3)(2x-1)(2x+1)}=\dfrac{6(4x+1)}{x(2x+1)}$

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.