Question

How do you simplify and state the restrictions for `(p^2-3p-10)/(p^2+p-2)`?

Answer 1

`(-p^2-3p-10)/((p+2)*(p-1))`

Explanation:

Using that `p^2+p-2=(p+2)(p-1)` we get the result above.

Answer 2

`(p-5)/(p-1)`

Explanation:

`"factorise numerator/denominator abd cancel any "`
`"common factors"`

`color(blue)"numerator"`

`"the factors of - 10 which sum to - 3 are - 5 and + 2"`

`p^2-3p-10=(p-5)(p+2)`

`color(blue)"denominator"`

`"the factors of - 2 which sum to + 1 are + 2 and - 1"`

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

`(p^2-3p-10)/(p^2+p-2)`

`=((p-5)cancel((p+2)))/(cancel((p+2))(p-1))=(p-5)/(p-1)`

`"the denominator cannot equal zero as this would make"`
`"the fraction undefined"`

`p-1!=0rArrp!=1`