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

1 Answer
Oct 18, 2015

(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)