Question

In the following exercises, divide the rational expressions.

$\frac{10+w}{w-8}÷\frac{100-w^2}{8-w}$

Short answer

The solution is$\frac{-1}{10-w}.$

Step-by-step solution

Step 1. Given InformationFlip the second rational expression

We have

$\frac{10+w}{w-8}÷\frac{100-w^2}{8-w}=\frac{10+w}{w-8}\times \frac{8-w}{100-w^2}$

Step 2. Factor the numerators and denominators

$$\begin{gathered} \frac{10+w}{w-8}\times \frac{8-w}{\left(10-w\right)\left(10+w\right)} \\ =\frac{-\left(10+w\right)\left(w-8\right)}{\left(w-8\right)\left(10-w\right)\left(10+w\right)} \end{gathered}$$

Step 3. Remove the common factor and simplify

$=\frac{-1}{10-w}$