SOLUTION: Find the domain of the rational function: f(x) = (2x^2 - 4) / (3x^2 + 6x - 45)

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Question 59178: Find the domain of the rational function:
f(x) = (2x^2 - 4) / (3x^2 + 6x - 45)
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Find the domain of the rational function:
f%28x%29=%282x%5E2-4%29%2F%283x%5E2%2B6x-45%29
The domain of a simple rational function is all real numbers EXCEPT the numbers that make the denominator equal 0.
3x%5E2%2B6x-45=0
3%28x%5E2%2B2x-15%29=0
%283%2F3%29%28x%5E2%2B2x-15%29=0%2F3
x%5E2%2B2x-15=0
(x+5)(x-3)=0
x+5=0 and x-3=0
x=-5 and x=3 will make the denominator 0 and the fraction undefined.
Therefore the domain includes all real numbers except:-5, and 3.
set builder notation:{x|x not= -5,3}
interval notation:(-infinity,-5)U(-5,3)U(3,infinity)
Happy Calcualting!!!