Question

How do you simplify `\frac { p ^ { 2} + 2p - 24} { p ^ { 2} + 5p - 6}`?

Answer 1

`(p^2+2p-24)/(p^2+5p-6) = (p-4)/(p-1) = 1-3/(p-1)`

with exclusion `p != -6`

Explanation:

Note that: `6*4=24` and `6-4=2`

Also: `6*1=6` and `6-1=5`

Hence we find:

`(p^2+2p-24)/(p^2+5p-6) = (color(red)(cancel(color(black)((p+6))))(p-4))/(color(red)(cancel(color(black)((p+6))))(p-1)) = (p-4)/(p-1) = (p-1-3)/(p-1) = 1-3/(p-1)`

with exclusion `p != -6`