SOLUTION: Hello once more. The question for today is: x^2/x-3 - 9/x-3 (these are dealing with adding and subtracting like rational expressions.) I know this so far:

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Question 106091This question is from textbook Beginning Algebra
: Hello once more. The question for today is:
x^2/x-3 - 9/x-3
(these are dealing with adding and subtracting like rational expressions.)
I know this so far:
x^2/x-3 - 9/x-3 = x^2-9/x-3.
I am usure of what to do with the numerator x^2-9.
I know that I cannot factor and simplify x^2-9 because there are no common factors between.
I think I should leave the final answer (because they just want us to write it in the simplest form as:
x^2-9/x-3.
Am I even close, or way off base?
I know that This question is from textbook Beginning Algebra

Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
x^2/x-3 - 9/x-3
= [x^2-9]/(x-3)
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This numerator can be factored:
= [(x+3)(x-3)]/(x-3)
Cancel the factor common to numerator and denominator to get:
= x+3
============
Cheers,
Stan H.

Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
You're here.

You're not way off. But you are a little off.
You can simplify by factoring.
Hint : Use the denominator as one factor.

If you expand the right hand side using the FOIL method, you can compare terms, find "a" and move forward.
If you get stuck, post another question.