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
is that finding the factors is harder.
is a difference of squares (since
so it can be factored using the pattern for a difference of squares,
, 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:
So the factored fraction is:
We can now see that there is a common factor, (x-3), that we can cancel:
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!