Question

Divide Rational Expressions:$\frac{7+x}{x-6}÷\frac{49-x^2}{x+6}$

Short answer

The required answer is$\frac{x+6}{\left(x-6\right)\left(7-x\right)}$.

Step-by-step solution

Step 1. Given information.

The given expression is

$\frac{7+x}{x-6}÷\frac{49-x^2}{x+6}$

Step 2.  Simplify the expression. 

$$\begin{gathered} \frac{7+x}{x-6}÷\frac{49-x^2}{x+6} \\ =\frac{\frac{7+x}{x-6}}{\frac{49-x^2}{x+6}} \end{gathered}$$

Apply the fraction rule.

$$\begin{gathered} =\frac{\left(7+x\right)\left(x+6\right)}{\left(x-6\right)\left(49-x^2\right)} \\ =\frac{x+6}{\left(x-6\right)\left(7-x\right)} \end{gathered}$$