Question

Which rational expression should be added to $\frac{x-x^2+2}{x(x^2-1)}$ to get $\frac{x+1}{x^2-1}$?

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

Answer 1

The correct option is B $\frac{2}{x}$

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