Question

In the following exercises, divide.

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

Short answer

The required answer is$-\frac{1}{v+5}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

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

Step 2. Simplify the expression.

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

Rewrite the division as the product of the first rational expression and the reciprocal of the second.

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

Factor the numerators and denominators and then multiply.

$-\frac{\left(v-5\right)\left(v-11\right)}{\left(v-11\right)\left(v+5\right)\left(v-5\right)}$

Simplify by dividing out common factors.

$-\frac{1}{v+5}$