## Algebra: A Combined Approach (4th Edition)

$\dfrac{3}{x^{2}+2x-8}+\dfrac{2}{x^{2}-3x+2}=\dfrac{5(x+1)}{(x+4)(x-2)(x-1)}$
$\dfrac{3}{x^{2}+2x-8}+\dfrac{2}{x^{2}-3x+2}$ Factor both denominators: $\dfrac{3}{(x+4)(x-2)}+\dfrac{2}{(x-2)(x-1)}=...$ Evaluate the sum: $...=\dfrac{3(x-1)+2(x+4)}{(x+4)(x-2)(x-1)}=\dfrac{3x-3+2x+8}{(x+4)(x-2)(x-1)}=...$ $...=\dfrac{5x+5}{(x+4)(x-2)(x-1)}=...$ Take out common factor $5$ to provide a more simplified answer: $...=\dfrac{5(x+1)}{(x+4)(x-2)(x-1)}$