Question

Simplify: $\frac{x-1}{x+1}+\frac{x+1}{x-1}-\frac{x^2+1}{x^2-1}$

• A. $\frac{x^2}{x^2-1}$
• B. $\frac{x+1}{x-1}$
• C. $\frac{x^2+1}{x^2-1}$
• D. 1

Answer 1

Answer: (C)

$\frac{x-1}{x+1}+\frac{x+1}{x-1}-\frac{x^2+1}{x^2-1}$
$=\frac{(x-1{)}^2+(x+1{)}^2-\left(x^2+1\right)}{x^2-1}$
$=\frac{(x-1{)}^2+(x+1{)}^2-x^2-1}{x^2-1}=\frac{x^2+1}{x^2-1}$