Answer
The answer is $-\frac{x+1}{x-1}$.
Work Step by Step
The given expressions is
$\frac{\frac{1}{x-1}+1}{\frac{1}{x+1}-1}$
Multiply and divide $1$ by $x-1$ in the numerator and $x+1$ in the denominator as show below.
$\frac{\frac{1}{x-1}+\frac{x-1}{x-1}}{\frac{1}{x+1}-\frac{x+1}{x+1}}$
Add and subtract as shown below.
$\frac{\frac{1+x-1}{x-1}}{\frac{1-x-1}{x+1}}$
Simplify.
$\frac{\frac{x}{x-1}}{\frac{-x}{x+1}}$
Convert divide into multiplication.
$\frac{x}{x-1}\cdot \frac{x+1}{-x}$
Simplify.
$-\frac{x+1}{x-1}$.
