SOLUTION: Identify any excluded values. Then simplify the expression. 9x^3-27x^2 over 12x-36 I identified the excluded value as x=3. I don't know what to do from here. Help!

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Question 181768This question is from textbook saxon algebra 2
: Identify any excluded values. Then simplify the expression.
9x^3-27x^2 over 12x-36
I identified the excluded value as x=3.
I don't know what to do from here. Help! This question is from textbook saxon algebra 2

Found 2 solutions by Earlsdon, solver91311:
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
You are correct on the excluded value of x = 3 because that's the value of x that would make the denominator zero and this, of course, is a no-no in math.
Now to simplify:
Factor from the numerator and factor from the denominator.
Cancel the indicated factors.
Reduce the fraction to...

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

You have correctly identified the excluded value, namely 3.

Now you need to factor both the numerator and denominator expressions.

In the numerator you have at least two factors of 3 in each term (or one factor of 9, if you prefer) and at least two factors of x in each term. In the denominator, you have one factor of 12 in each term. So:

Now you can eliminate the factor of common to both numerator and denominator to leave you with:

which is true if and only if

It is important to note that if

That's because if , while is undefined.

If you graph , you would get something that looks very much like a parabola with vertex at the origin, but there would be a hole in the graph at

John