Answer
$\frac{1}{x} + \frac{-1}{x+1}$
Work Step by Step
We must first find the Partial Fraction Decomposition:
$\frac{A}{x} + \frac{B}{x+1} = \frac{1}{x^{2} + x}$
We must then solve for the constants:
$A(x + 1) + Bx = 1$
$Ax + A + Bx = 1$
$Ax + Bx = 0$
$A = 1$
So:
$B = -1$
The Partial Fraction is:
$\frac{1}{x} + \frac{-1}{x+1}$
Checking the Result:
$\frac{x+1 - x}{x(x+1)} = \frac{1}{x(x+1)} = \frac{1}{x^{2} + x}$
