Answer
$ \frac{x^2+6x-4}{x^2+6 x+1}$.
Work Step by Step
The given expression is
$=\frac{x-\frac{4}{x+6}}{\frac{1}{x+6}+x}$
Multiply both the numerator and denominator by $(x+6)$.
$=\frac{(x+6)}{(x+6)} \cdot \frac{x-\frac{4}{x+6}}{\frac{1}{x+6}+x}$
Use the distributive property.
$= \frac{(x+6) \cdot x-(x+6) \cdot\frac{4}{x+6}}{(x+6) \cdot\frac{1}{x+6}+(x+6) \cdot x}$
Simplify.
$= \frac{x^2+6x-4}{1+x^2+6 x}$.
Rearrange.
$= \frac{x^2+6x-4}{x^2+6 x+1}$.
