Question

Subtract Rational Expressions with a Common Denominator

In the following exercises, subtract.

$\frac{d^2}{d+4}-\frac{3d+28}{d+4}.$

Short answer

The answer is$(d-7).$

Step-by-step solution

Step 1. Given Information.

Given:

$\frac{d^2}{d+4}-\frac{3d+28}{d+4}$ having the same denominator.

Step 2. Solving the expression given.

$$\begin{gathered} Asthedenominatorissamesowecandirectlysubtractthenumerators: \\ \frac{d^2}{d+4}-\frac{3d+28}{d+4}=\frac{d^2-(3d+28)}{d+4}=\frac{d^2-3d-28}{d+4} \\ =\frac{(d+4)(d-7)}{d+4}=d-7. \end{gathered}$$