Question

Find the partial fraction decomposition of

Answer 1

`\frac1{x(x-1)}=\frac ax+\frac 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

`\frac1{x(x-1)}=\frac1{x-1}-\frac1x`