Question

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

Answer 1

`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]}