SOLUTION: What is one minus m squared over m minus one ?

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Question 709999: What is one minus m squared over m minus one ?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%281-m%29%2F%28m%5E2-1%29
When reducing fractions only factors will cancel. So to see if this fraction will reduce we must first see what the factors of the numerator and denominator are. The numerator will not factor except we can factor out a 1. The denominator is a difference of squares which we can factor using the pattern: a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29.
%281%2A%281-m%29%29%2F%28m%2B1%29%28m-1%29%29

At first glance it doesn't look like there are factors to cancel. However 1-m and m-1 are opposites/negatives of each other! So if we factor out a -1 from one of them, then they will match.
%28-1%2A%28m-1%29%29%2F%28m%2B1%29%28m-1%29%29
(Note: Make sure you see how the numerator, if multiplied out, will be -m+1 which is equal to 1-m.) Now that we have a factor in the numerator that matches a factor in the denominator we can cancel them:
%28-1%2Across%28%28m-1%29%29%29%2F%28m%2B1%29cross%28%28m-1%29%29%29
leaving:
%28-1%29%2F%28m%2B1%29
or
-1%2F%28m%2B1%29

P.S. Note: The 1's in our final fraction cannot be canceled! The 1 in the denominator is not a factor of the denominator so it cannot be canceled. Only factors cancel!