Answer
$\frac{3}{2(x-4)}-\frac{3}{2x}$
Work Step by Step
1. Let $\frac{6}{x(x-4)}=\frac{A}{x}+\frac{B}{x-4}$
2. Combine the right side to get $\frac{Ax-4A+Bx}{x(x-4)}=\frac{(A+B)x-4A}{x(x-4)}$
3. Compare with step 1, we have $A+B=0$ and $-4A=6$, thus $A=-\frac{3}{2}$ and $B=\frac{3}{2}$
4. We have $\frac{6}{x(x-4)}=\frac{3}{2(x-4)}-\frac{3}{2x}$
