SOLUTION: Simplify x^2-9 ----- x^2-6+9

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Question 347460: Simplify
x^2-9
-----
x^2-6+9
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
To simplify (or reduce) a fraction, you look for common factors to cancel. This has been true since the "good old days" of fractions like 2/4. The only thing different with fractions like %28x%5E2-9%29%2F%28x%5E2-6x%2B9%29 is that finding the factors is harder.

Your numerator, x%5E2-9 is a difference of squares (since 9+=+3%5E3 so it can be factored using the pattern for a difference of squares, a%5E2+-+b%5E2+=+%28a%2Bb%29%28a-b%29, with "a" being x and "b" being 3. So your nuerator factors into (x+3)(x-3).

In the denominator, we look for factors of 9 that add up to -6. The only pair of factors of 9 that add up to -6 are: -3 and -3. So the denominator factors into: %28x-3%29%28x-3%29

So the factored fraction is:
%28%28x%2B3%29%28x-3%29%29%2F%28%28x-3%29%28x-3%29%29
We can now see that there is a common factor, (x-3), that we can cancel:
%28%28x%2B3%29cross%28%28x-3%29%29%29%2F%28cross%28%28x-3%29%29%28x-3%29%29
leaving
%28x%2B3%29%2F%28x-3%29
which is the simplified/reduced fraction. (Don't try to cancel an x or a 3 here. They are not factors and only factors can be canceled!)