Algebra: A Combined Approach (4th Edition)

$\dfrac{3x+4y}{x^{2}+4xy+4y^{2}}\cdot\dfrac{x+2y}{2}=\dfrac{3x+4y}{2(x+2y)}$
$\dfrac{3x+4y}{x^{2}+4xy+4y^{2}}\cdot\dfrac{x+2y}{2}$ 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: $...=\dfrac{(3x+4y)(x+2y)}{2(x+2y)^{2}}=\dfrac{3x+4y}{2(x+2y)}$