Answer
$\displaystyle \frac{x+1}{x-1}$
Work Step by Step
$\displaystyle \frac{1+\frac{1}{x}}{1-\frac{1}{x}}=(1+\frac{1}{x})\div(1-\frac{1}{x})$
$=(\displaystyle \frac{x}{x}+\frac{1}{x})\div(\frac{x}{x}-\frac{1}{x})$
$=\displaystyle \frac{x+1}{x}\div\frac{x-1}{x}$
... division = multiplication with the reciprocal,
$=\displaystyle \frac{x+1}{x}\cdot\frac{x}{x-1}$
... x cancels,
$=\displaystyle \frac{x+1}{x-1}$
