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