SOLUTION: (x^2-9)/(2x-6)

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Question 93247: (x^2-9)/(2x-6)
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
%28x%5E2-9%29%2F%282x-6%29
.
Note that the numerator is the difference of two squares. As such it can be factored
using the following rule:
.
A%5E2+-+B%5E2+=+%28A-B%29%2A%28A%2BB%29
.
This form is identical to the numerator in the given expression if you let A = x and B = 3.
Substituting these into the rule you get:
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%28x%5E2+-+9%29+=+x%5E2+-+3%5E2+=+%28x-3%29%2A%28x%2B3%29
.
So in place of x%5E2+-+9 you can substitute %28x-3%29%2A%28x%2B3%29 to convert the given
expression to:
.
%28%28x-3%29%2A%28x%2B3%29%29%2F%282x-6%29
.
Then notice that the denominator can be factored because 2 is common to both terms in
the denominator. When you factor the 2 you then have:
.
%28%28x-3%29%2A%28x%2B3%29%29%2F%282%28x-3%29%29
.
Then you can cancel the term in the denominator that is common with the one in the numerator
to get:
.
%28%28cross%28x-3%29%29%2A%28x%2B3%29%29%2F%282%2A%28cross%28x-3%29%29%29
.
and what remains is:
.
%28x%2B3%29%2F2
.
This is the answer to the problem.
.
Hope this helps you to understand a method for reducing the problem to a lower form.