Answer
$\frac{2x+7}{x^2-4}$.
Work Step by Step
The given expression is
$=\frac{2}{x-2}+\frac{3}{x^2-4}$
$=\frac{2}{x-2}+\frac{3}{x^2-2^2}$
Use the special formula $A^2-B^2=(A-B)(A+B)$
$=\frac{2}{x-2}+\frac{3}{(x-2)(x+2)}$
The LCD is $(x-2)(x+2)$.
Multiply each numerator and denominator by the extra factor to form the LCD.
$=\frac{2(x+2)}{(x-2)(x+2)}+\frac{3}{(x-2)(x+2)}$
Add numerators because denominators are equal.
$=\frac{2(x+2)+3}{(x-2)(x+2)}$
Use the distributive property.
$=\frac{2x+4+3}{(x-2)(x+2)}$
Simplify.
$=\frac{2x+7}{(x-2)(x+2)}$
Use the special formula $(A-B)(A+B)=A^2-B^2$
$=\frac{2x+7}{x^2-2^2}$
Simplify.
$=\frac{2x+7}{x^2-4}$.
