Answer
$\frac{-x^{2}+10x+19}{(x+3)(x+1)(x-2)}$
Work Step by Step
Original Equation
$\frac{7}{x^{2}-x-2}$ - $\frac{x-1}{x^{2}+4x+3}$
Factor Denominator
$\frac{7}{(x-2)(x+1)}$ - $\frac{x-1}{(x+3)(x+1)}$
Find LCD: (x+3)(x+1)(x-2)
Add numerators
$\frac{7(x+3)-(x-1)(x-2)}{(x+3)(x+1)(x-2)}$
Simplify
Answer: $\frac{-x^{2}+10x+19}{(x+3)(x+1)(x-2)}$
