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

$\dfrac{4}{3x^{2}+8x-3}+\dfrac{2}{3x^{2}-7x+2}=\dfrac{2}{(x+3)(x-2)}$
$\dfrac{4}{3x^{2}+8x-3}+\dfrac{2}{3x^{2}-7x+2}$ Factor both denominators: $\dfrac{4}{(x+3)(3x-1)}+\dfrac{2}{(3x-1)(x-2)}=...$ Evaluate the sum: $...=\dfrac{4(x-2)+2(x+3)}{(x+3)(x-2)(3x-1)}=\dfrac{4x-8+2x+6}{(x+3)(x-2)(3x-1)}=...$ $...=\dfrac{6x-2}{(x+3)(x-2)(3x-1)}=...$ Take out common factor $2$ from the numerator and simplify: $...=\dfrac{2(3x-1)}{(x+3)(x-2)(3x-1)}=\dfrac{2}{(x+3)(x-2)}$