Question

Add Rational Expressions with a Common Denominator

In the following exercises, add.

$\frac{p^2+10p}{p+5}+\frac{25}{p+5}.$

Short answer

The answer is$p+5.$

Step-by-step solution

Step 1. Given Information.

Given:

$\frac{p^2+10p}{p+5}+\frac{25}{p+5}$having the same denominator.

Step 2. Formula used for calculation.

$a^2+2ab+b^2={\left(a+b\right)}^2.$

Step 3. Solving the expression given.

$$\begin{gathered} Asthedenominatorissamewecandirectlyaddthenumerators: \\ \frac{p^2+10p}{p+5}+\frac{25}{p+5}=\frac{p^2+10p+25}{p+5}. \\ Nowu\sin gtheformulagiveninstep2weget, \\ =\frac{{\left(p+5\right)}^2}{(p+5)}=p+5. \end{gathered}$$