Question

Simplify $\frac{x+2}{x+3}+\frac{x-1}{x-2}.$

• A. $\frac{2x^2+2x-7}{x^2+x-6}$
• B. $\frac{2x^2+2x-7}{x^2+x+6}$
• C. $\frac{2x^2+2x-7}{x^2-x+6}$
• D. $\frac{2x^2+2x+7}{x^2+x+6}$

Answer 1

The correct option is A $\frac{2x^2+2x-7}{x^2+x-6}$

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

$=\frac{x^2-4+x^2+2x-3}{x^2+x-6}$

$=\frac{2x^2+2x-7}{x^2+x-6}$