SOLUTION: 14b-21 _______ 15-10b This is an exercise for a test. I would very much appreciate the answer as it could help to understand others that are similar.

Algebra ->  Expressions-with-variables -> SOLUTION: 14b-21 _______ 15-10b This is an exercise for a test. I would very much appreciate the answer as it could help to understand others that are similar.      Log On


   

Question 129595: 14b-21
_______
15-10b

This is an exercise for a test. I would very much appreciate the answer as it could help to understand others that are similar.
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
%2814b-21%29%2F%2815-10b%29
.
If you see fractions of this form, look at how you can factor the numerator and the denominator.
When you factor them, hopefully they will contain common terms. If the same factor appears in
both the numerator and denominator, the factor can be canceled in both places.
.
In this case, note that a factor of 7 is common to both terms in the numerator, and a factor
of 5 is common to both terms in the denominator. After you do the factoring you have:
.
%287%2A%282b-3%29%29%2F%285%2A%283-2b%29%29
.
In the bottom set of parentheses, reverse the order of the 2b and the 3 and you have:
.
%287%2A%282b-3%29%29%2F%285%2A%28-2b%2B3%29%29
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Then factor -1 from the bottom set of parentheses and you have:
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%287%2A%282b-3%29%29%2F%285%2A%28-1%29%2A%282b-3%29%29
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Notice now that you have %282b-3%29in both the numerator and the denominator. Cancel these
common terms:
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%287%2A%28cross%282b-3%29%29%29%2F%285%2A%28-1%29%2A%28cross%282b-3%29%29%29
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and you are left with:
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7%2F%285%2A%28-1%29%29
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and this multiplies out to give:
.
-7%2F5
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Hope this helps you with your other problems.
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