Answer
$\dfrac{15}{x^{2}+6x+9}+\dfrac{2}{x+3}=\dfrac{2x+21}{(x+3)^{2}}$
Work Step by Step
$\dfrac{15}{x^{2}+6x+9}+\dfrac{2}{x+3}$
Factor the denominator of the first fraction, which is a perfect square trinomial:
$\dfrac{15}{x^{2}+6x+9}+\dfrac{2}{x+3}=\dfrac{15}{(x+3)^{2}}+\dfrac{2}{x+3}=...$
Evaluate the sum of the two rational expressions and simplify:
$...=\dfrac{15+2(x+3)}{(x+3)^{2}}=\dfrac{15+2x+6}{(x+3)^{2}}=\dfrac{2x+21}{(x+3)^{2}}$
