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(x2 - 9) / (x2 + 3) does not have a simple solution. Perhaps the question you were actually looking to have answered was:

(x2 - 9) / (x + 3)

Which is equal to (x - 3). This is called a difference of squares, where any time you see a term in the format:

(x2 - b2)

You know that it is equal to (x + b)(x - b). Of course, (x + b)(x - b) / (x + b) will be equal to (x - b), giving you the answer above.

If on the other hand, you are indeed looking for the answer to (x2 - 9) / (x2 + 3), you could try long division. That will give you 1 with a remainder of negative twelve, or:

1 + 12/(x2 + 3)

Alternately, if you have a value for the term, you can solve the equation:

(x2 - 9) / (x + 3) = a

x2 - 9 = ax + 3a

x2 - ax = 9 + 3a

x2 - ax + (a/2)2 = 9 + 3a + (a/2)2 ← this is called "completing the square".

(x - (a/2))2 = 9 + 3a + (a/2)2

x - (a/2) = [9 + 3a + (a/2)2]1/2

x = [9 + 3a + (a/2)2]1/2 + a/2

You can then plug in whatever value is given for 'a'. For example, if it's equal to zero:

x = [9 + 3(0) + (0/2)2]1/2 + 0/2

x = (9 + 0 + 0)1/2 + 0

x = 91/2

x = 3

Note that x can not be equal to negative three, as that would cause division by zero in the original equation.

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Q: X2 - 9 divided by x2 3?
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