Answer
$\frac{-1}{x} + \frac{1}{x-3}$
Work Step by Step
We must first find the Partial Fraction Decomposition:
$\frac{A}{x} + \frac{B}{x-3} = \frac{3}{x^{2} -3x}$
We must then solve for the constants:
$A(x-3) + Bx = 3$
$Ax - 3A + Bx = 3$
$Ax + Bx = 0$
$-3A = 3$
$A = -1$
$-1 + B = 0$
$B = 1$
The Partial Fraction is:
$\frac{-1}{x} + \frac{1}{x-3}$
Checking the Result:
$\frac{-1(x-3) + x}{x(x-3)} = \frac{-x + 3 + x}{x(x-3)} = \frac{3}{x^{2}-3x}$
Therefore, the answer is correct.
