SOLUTION: Simplify X^2-x/X^2-1

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Question 384242: Simplify
X^2-x/X^2-1
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-x%29%2F%28x%5E2-1%29
To simplify (or reduce) a fraction we cancel common factors in the numerator and denominator, if any. And to do this we need to know what the factors are. So we start by factoring.

The numerator has a common factor of x and the denominator fits the difference of squares pattern:
%28x%28x-1%29%29%2F%28%28x%2B1%29%28x-1%29%29
We can now see that (x-1) is a factor in both the numerator and denominator which we can cancel:
%28x%2Across%28%28x-1%29%29%29%2F%28%28x%2B1%29cross%28%28x-1%29%29%29
leaving:
x%2F%28x%2B1%29
This is the simplified fraction. (Note: The x's do not cancel. Only factors can be canceled! And the x in the denominator is not a factor.)