Question

Find the partial fraction decomposition of

Answer 1

$\dfrac1{x(x-1)}=\dfrac ax+\dfrac b{x-1}$

$1=a(x-1)+bx$

If $x=0$, then

$1=-a\implies a=-1$

If $x=1$, then

$1=b$

So we have

$\dfrac1{x(x-1)}=\dfrac1{x-1}-\dfrac1x$