Question

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

• A. 1
• B. 2
• C. 0.0
• D. None of the above

Answer 1

The correct option is A 1

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

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

= $\frac{x^2+2x-1}{x^2-1}-\frac{2x}{x^2-1}$

= $\frac{x^2-1}{x^2-1}$ = 1