Answer
$\frac{5(x^{2}+x-4)}{(3x+2)(x+3)(2x-5)}$
Work Step by Step
Original Equation
$\frac{x+4}{3x^{2}+11x+6}$ + $\frac{x}{2x^{2}+x-15}$
Factor Denominator
$\frac{x+4}{(3x+2)(x+3)}$ + $\frac{x}{(2x-5)(x+3)}$
Find LCD: (3x+2)(x+3)(2x-5)
Add numerators
$\frac{(x+4)(2x-5)+x(3x+2)}{(3x+2)(x+3)(2x-5)}$
Simplify
$\frac{5x^{2}+5x-20}{(3x+2)(x+3)(2x-5)}$
Factor
Answer: $\frac{5(x^{2}+x-4)}{(3x+2)(x+3)(2x-5)}$
