Answer
$\dfrac{2}{x-1}-\dfrac{6}{3x-2} $
Work Step by Step
We will write the partial decomposition as:
$\dfrac{2}{(x-1)(3x-2)}=\dfrac{A}{x-1}+\dfrac{B}{3x-2} ~~~~(a)$
This implies that $2=A(3x-2)+B (x-1)$
Plug $x=1$ to obtain: $A=2$
Now, plug $x=\dfrac{3}{2}$ to obtain: $B=-6$
So, the equation (a) becomes:
$\dfrac{2}{(x-1)(3x-2)}=\dfrac{2}{x-1}-\dfrac{6}{3x-2} $
