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

1 Answer
Oct 18, 2015

Answer:

#(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)