Answer
$\dfrac{5}{3x}-\dfrac{10}{3(2x+1)} $
Work Step by Step
We will write the partial decomposition as:
$\dfrac{5}{3x(2x+1)}=\dfrac{A}{3x}+\dfrac{B}{2x+1} ~~~~(a)$
This implies that $5=A(2x+1)+B (3x)$
Plug $x=0$ to obtain: $A=5$
Now, plug $x=\dfrac{-1}{2}$ to obtain: $B=\dfrac{-10}{3}$
So, the equation (a) becomes:
$\dfrac{5}{3x(2x+1)}=\dfrac{5}{3x}-\dfrac{10}{3(2x+1)} $
