Answer
$\dfrac{3x+4y}{x^{2}+4xy+4y^{2}}\cdot\dfrac{x+2y}{2}=\dfrac{3x+4y}{2(x+2y)}$
Work Step by Step
$\dfrac{3x+4y}{x^{2}+4xy+4y^{2}}\cdot\dfrac{x+2y}{2}$
Factor the denominator of the first fraction, which is a perfect square trinomial:
$\dfrac{3x+4y}{x^{2}+4xy+4y^{2}}\cdot\dfrac{x+2y}{2}=\dfrac{3x+4y}{(x+2y)^{2}}\cdot\dfrac{x+2y}{2}=...$
Evaluate the product of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression:
$...=\dfrac{(3x+4y)(x+2y)}{2(x+2y)^{2}}=\dfrac{3x+4y}{2(x+2y)}$
