Answer
$\frac{1+x}{1-x}$.
Work Step by Step
The given expression is
$=\frac{x^{-2}+x^{-1}}{x^{-2}-x^{-1}}$
Multiply and divide the fraction by $x^2$.
$=\frac{x^2}{x^2} \cdot \frac{x^{-2}+x^{-1}}{x^{-2}-x^{-1}}$
Use the distributive property.
$= \frac{x^2 \cdot x^{-2}+x^2 \cdot x^{-1}}{x^2 \cdot x^{-2}-x^2 \cdot x^{-1}}$
Add powers of the same base.
$= \frac{x^{-2+2}+x^{-1+2}}{x^{-2+2}-x^{-1+2}}$
Simplify.
$= \frac{x^{0}+x^{1}}{x^{0}-x^{1}}$
$= \frac{1+x}{1-x}$.
