Answer
$\dfrac{4}{x(1-x)}=\dfrac{4}{x}+\dfrac{4}{1-x} $
Work Step by Step
We will write the partial decomposition as:
$\dfrac{4}{x(1-x)}=\dfrac{A}{x}+\dfrac{B}{1-x} ~~~~(a)$
This implies that $4=A(1-x)+Bx$
Plug $x=0$ to obtain: $A=4$
Now, plug $x=1$ to obtain: $B=4$
So, the equation (a) becomes:
$\dfrac{4}{x(1-x)}=\dfrac{4}{x}+\dfrac{4}{1-x} $
