SOLUTION: Perform the indicated operation. Simplify if possible 5x/x^2-7x+10 - 10/x^2-7x+10

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Perform the indicated operation. Simplify if possible 5x/x^2-7x+10 - 10/x^2-7x+10      Log On


   



Question 95841: Perform the indicated operation. Simplify if possible
5x/x^2-7x+10 - 10/x^2-7x+10

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given to simplify:
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%285x%2F%28x%5E2-7x%2B10%29%29++-++%2810%2F%28x%5E2-7x%2B10%29%29
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Notice that the two fractions have a common denominator. Therefore their numerators
can be combined over the common denominator. When you do that the given polynomial becomes:
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%285x+-+10%29%2F%28x%5E2+-7x+%2B+10%29
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Next notice that in the numerator both terms have a common factor of 5. So factor the numerator
and the polynomial then becomes:
.
%285%28x+-+2%29%29%2F%28x%5E2+-7x%2B10%29
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Then observe that the denominator can be factored to %28x+-+5%29%28x-2%29. Substitute this
factored form for the denominator and you have:
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%285%28x-2%29%29%2F%28%28x-5%29%28x-2%29%29
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There is a common term in the denominator and the numerator. Cancel this common term:
.
%285%28cross%28x-2%29%29%29%2F%28%28x-5%29%28cross%28x-2%29%29%29
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and you are left with the simplified form:
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5%2F%28x-5%29
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No further simplification is needed. This is your answer.
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Hope this helps you to understand the problem and how to work it.
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