Answer
$-x-1$
Work Step by Step
Simplifying Rational Expressions
1. Factor the numerator and the denominator completely.
2. Divide both the numerator and the denominator by any common factors.
---
Numerator = difference of squares = $(x+1)(x-1)$
Denominator = $-(x-1)$
Expression = $\displaystyle \frac{(x+1)(x-1)}{ -(x-1)}$
... divide both with the common factor: $(x-1)$
Expression = $\displaystyle \frac{x+1}{-1}$ = $-(x+1) =-x-1$
