Question

In the following exercises, divide the rational expressions.

$\frac{v-5}{11-v}÷\frac{v^2-25}{v-11}$

Short answer

The simplified rational expression is$\frac{-1}{v+5}$

Step-by-step solution

Step 1. Given information

We have $\frac{v-5}{11-v}÷\frac{v^2-25}{v-11}$

Flip the second rational expression

$\frac{v-5}{11-v}\times \frac{v-11}{v^2-25}$

Step 2. Factor the numerators and denominators

$$\begin{gathered} \frac{v-5}{11-v}\times \frac{v-11}{\left(v-5\right)\left(v+5\right)} \\ =\frac{-\left(v-5\right)\left(11-v\right)}{\left(11-v\right)\left(v-5\right)\left(v+5\right)} \end{gathered}$$

Step 3. Remove the common factors and simplify

$=\frac{-1}{\left(v+5\right)}$