How do you simplify #(x^2 – x – 6 )/(x^2 – 9x + 18 )#?

1 Answer
Apr 23, 2016

Answer:

#(x^2-x-6)/(x^2-9x+18)=(x+2)/(x-6)=1+8/(x-6)#

excluding #x=3#

Explanation:

Factor the numerator and denominator. Cancel the common factor #(x-3)#, noting that #x=3# is an excluded value. Simplify...

#(x^2-x-6)/(x^2-9x+18)#

#=(color(red)(cancel(color(black)((x-3))))(x+2))/(color(red)(cancel(color(black)((x-3))))(x-6))#

#=(x+2)/(x-6)#

#=(x-6+8)/(x-6)#

#=1+8/(x-6)#

excluding #x=3#.

The value #x=3# must be excluded since the numerator and denominator of the original rational expression are both zero, resulting in an undefined value, whereas the simplified expression is well defined when #x=3#.