SOLUTION: How do you simplify and then find the domain for the rational function: (9x^2-36)/(x+2)

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Question 817077: How do you simplify and then find the domain for the rational function:
(9x^2-36)/(x+2)
Found 2 solutions by josgarithmetic, doodles:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Careful! If you simplify the expression, then that is a different function.
r%28x%29=%289x%5E2-36%29%2F%28x%2B2%29
%289x%5E2-36%29%2F%28x%2B2%29
%289%2A%28x%5E2-4%29%29%2F%28x%2B2%29
r%28x%29=9%28%28x%2B2%29%28x-2%29%29%2F%28x%2B2%29
As simplifed,
f%28x%29=9%28x-2%29

r(x) and f(x) are different functions.
One is rational and the other is a line.
r(x) is undefined at x=-2;
the domain for r(x) is x%3C-2 and x%3E-2

Answer by doodles(24) About Me  (Show Source):
You can put this solution on YOUR website!
The domain is in essence defined by what x cannot be. In other words the denominator cannot not equal to 0, the reason being if the number the denominator is equal to 0 the answer is undefined. So, in this case
%289x%5E2-36%29%2F%28x%2B2%29
What number will make the denominator 0?
In this case if x = 2 then the denominator will equal 0. Thus x cannot equal 2. This is also your domain.
Now lets simplify.
+%289x%5E2-36%29+=+9+%28x%5E2-4%29+
So our factor for the numerator is:
+%289%29%28x-2%29%28x%2B2%29+
Now we divide by cancelling similar terms like so:
%289%29cross%28x%2B2%29%28x-2%29%2Fcross%28x%2B2%29
Ultimately, our final answer is:
%289%29%28x-2%29