## Intermediate Algebra for College Students (7th Edition)

The answer is $-\frac{x+1}{x-1}$.
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. $-\frac{x+1}{x-1}$.