SOLUTION: Simplify: x^2-10x+9 --------- x^2+2x-3

Question 347463: Simplify:
x^2-10x+9
---------
x^2+2x-3
Answer by jsmallt9(3758) (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 is that finding the factors is harder.

Factoring your numerator is a matter of finding the factors of 9 which add up to -10. In order for the product of the factors to be positive 9, they must be both positive or both negative. (Often the negative factors are forgotten.). And if the factors add up to negative 10 then they must both be negative (since you can't add two positives and get a negative). The only pairs of negative factors of 9 are: -3 and -3 or -1 and -9. Only -1 and -9 add up to -10 so you numerator factors into .

Using the same type of logic on the denominator, we look for factors of -3 that add up to +2. The only pair of factors of -3 that add up to +2 are: -1 and 3. So the denominator factors into:

So the factored fraction is:

We can now see that there is a common factor, (x-1), that we can cancel:

leaving

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!)
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