Question 95841
Given to simplify:
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{{{(5x/(x^2-7x+10))  -  (10/(x^2-7x+10))}}}
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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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{{{(5x - 10)/(x^2 -7x + 10)}}}
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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:
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{{{(5(x - 2))/(x^2 -7x+10)}}}
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Then observe that the denominator can be factored to {{{(x - 5)(x-2)}}}. Substitute this
factored form for the denominator and you have:
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{{{(5(x-2))/((x-5)(x-2))}}}
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There is a common term in the denominator and the numerator. Cancel this common term:
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{{{(5(cross(x-2)))/((x-5)(cross(x-2)))}}}
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and you are left with the simplified form:
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{{{5/(x-5)}}}
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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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