Question

Divide Rational Expressions:$\frac{10-w}{w-8}÷\frac{100-w^2}{8-w}$

Short answer

The required answer is$-\frac{1}{10+w}$.

Step-by-step solution

Step 1. Given information 

The given expression is$\frac{10-w}{w-8}÷\frac{100-w^2}{8-w}$.

Step 2.  Simplify the expression. 

$$\begin{gathered} \frac{10-w}{w-8}÷\frac{100-w^2}{8-w} \\ =\frac{\frac{10-w}{w-8}}{\frac{100-w^2}{8-w}} \end{gathered}$$

Apply the fraction rule.

$$\begin{gathered} =\frac{\left(10-w\right)\left(8-w\right)}{\left(w-8\right)\left(100-w^2\right)} \\ =-\frac{1}{10+w} \end{gathered}$$