\(\text{Find the domain of $\frac{x^2 + 10x + 21}{x^2 + 4x - 21}$. (Express your answer using interval notation.) }\)
Thanks!
The domain is only affected by the values of x that make the denominator 0
So....set x^2 + 4x - 21 = 0 to find these values
Factor as
(x + 7) ( x - 3) = 0 set each factor to 0 and solve for x and we have
x + 7 = 0 x - 3 = 0
x = - 7 x = 3
So the domain is all x except x = -7 and x = 3
In interval notation
( - infinity, -7) U (-7, 3) U ( 3, infinity )