Question

How do you simplify `(x^2+3x-18)/(x^2-36)`?

Answer 1

`(x^2 + 3x − 18) / (x^2 − 36) = (x - 3) / (x - 6)` only if x `!= -6`

Explanation:

`x^2 + 3x − 18` can be written as
`(x + 6) * (x - 3)` and
`x^2 − 36` can be written as `(x + 6) * (x - 6)`
So,
#(x^2 + 3x − 18) / (x^2 − 36) = ((x + 6) * (x - 3)) / ((x + 6) * (x - 6)) #
We can cancel `x + 6` only if `x + 6 != 0 or if x != -6`
If `x != -6`, the expression becomes
`(x - 3) / (x - 6)`
If x = -6, it is indeterminate ( 0 / 0 form)