Question

How do you simplify `(2-p)/(p^2-p-2)`?

Answer 1

`-1/(p+1)`

Explanation:

Well you have to do something so factorise the denominator
`(2-p)/((p-2)(p+1))`

And it helps
`-((p-2))/((p-2)(p+1))`

Cancel
`-1/(p+1`

Answer 2

`(-1)/(p+1)`

Explanation:

The first step is to factorise the denominator.

`rArrp^2-p-2`

Consider the factors of - 2 which sum to give the coefficient of the middle term, that is - 1.

These are - 2 and + 1 , since.

`(-2xx+1)=-2" and " -2+1=-1`

`rArrp^2-p-2=(p-2)(p+1)`

Fraction can now be expressed as `(2-p)/((p-2)(p+1))`

Take out a common factor of - 1 in the numerator.

`rArr2-p=-1(p-2)`

and now we have a fraction which may be simplified.

`rArr(-1cancel((p-2)))/(cancel((p-2))(p+1))=(-1)/(p+1)=-1/(p+1)`