Question

Reduce: $\frac{(x+1)(2x-3)}{x-1}+\frac{x+1}{x^2-1}$ into lowest form.

• A. $\frac{(2x^2-x-2)}{x-1}$
• B. $\frac{(x+1{)}^2(2x-3)}{x-1}$
• C. $\frac{(x+1)(x-3)}{x-1}$
• D. $\frac{(x+1)(2x-3)}{x+1}$

Answer 1

The correct option is A $\frac{(2x^2-x-2)}{x-1}$

$\frac{(x+1)(2x-3)}{x-1}+\frac{x+1}{x^2-1}$
$\frac{(x+1)(2x-3)}{x-1}+\frac{x+1}{x^2-1}=\frac{(x+1)(2x-3)}{x-1}+\frac{x+1}{(x+1)(x-1)}$
$=$ $\frac{(x+1)(2x-3)}{x-1}+\frac{1}{x-1}$
$=$ $\frac{(2x^2-x-2)}{x-1}$