Question

How do you express `3/((x-2)(x+1))` in partial fractions?

Answer 1

`1/(x-2)-1/(x+1)`

Explanation:

`3/[(x-2)(x+1)]=[(x+1)-(x-2)]/[(x-2)*(x+1)]=1/(x-2)-1/(x+1)`

Answer 2

`1/(x-2)-1/(x+1)`

Explanation:

Here,
`3/((x-2)(x+1))`
we have two factors in denominator: `(x-2) and (x+1)`.
We take, `color(red)((x+1)-(x-2))=x+1-x+2=color(red)(3`
`:.color(red)(3)/((x-2)(x+1))=(color(red)((x+1)-(x-2)))/((x-2)(x+1))`
`=cancel((x+1))/((x-2)cancel((x+1)))-cancel((x-2))/(cancel((x-2))(x+1))=1/(x-2)-1/(x+1)`