Question

Subtract Rational Expressions with a Common Denominator

In the following exercises, subtract.

$\frac{z^2}{z+10}-\frac{100}{z+10}.$

Short answer

The answer is$z-10$.

Step-by-step solution

Step 1. Given Information.

Given:

$\frac{z^2}{z+10}-\frac{100}{z+10}$having the same denominator.

Step 2. Solving the given expression.

$$\begin{gathered} Asthedenominatorissamesowecandirectlysubtractthenumerators: \\ \frac{z^2}{z+10}-\frac{100}{z+10} \\ =\frac{z^2-100}{z+10} \\ =\frac{(z+10)(z-10)}{z+10}=z-10. \end{gathered}$$