Question

Simplify the expression$\frac{6}{d^2+4d+4}+\frac{5}{d+2}$.

Short answer

The simplified value of expression is$\frac{16+5d}{{\left(d+2\right)}^2}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is$\frac{6}{d^2+4d+4}+\frac{5}{d+2}$.

Step 2. Simplify the expression.

The given expression $\frac{6}{d^2+4d+4}+\frac{5}{d+2}$is simplified as:

$\begin{array}{c}\frac{6}{d^2+4d+4}+\frac{5}{d+2}=\frac{6}{{\left(d+2\right)}^2}+\frac{5}{d+2}\\ =\frac{6+5\left(d+2\right)}{{\left(d+2\right)}^2}\\ =\frac{16+5d}{{\left(d+2\right)}^2}\end{array}$

Step 3. Conclusion.

The simplified value of expression is$\frac{16+5d}{{\left(d+2\right)}^2}$.