How do you find the domain of #(3x^2+3x-6)/(x^2-x-12)#?

1 Answer
Jan 7, 2018

Answer:

#x inRR,x!=-3,4#

Explanation:

The denominator of the rational expression cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the values that x cannot be.

#"solve "x^2-x-12=0rArr(x-4)(x+3)=0#

#rArrx=-3" or "x=4larrcolor(red)"excluded values"#

#rArr"domain is "x inRR,x!=-3,4#

#"in interval notation as"#

#(-oo,-3)uu(-3,4)uu(4,+oo)#
graph{(3x^2+3x-6)/(x^2-x-12) [-10, 10, -5, 5]}