SOLUTION: x+2 xsquare -5x +6 Dividing by a rational expression ____ divided ___________ _____ 7-x xsquare -9x +14

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Question 336427: x+2 xsquare -5x +6 Dividing by a rational expression
____ divided _________________
7-x xsquare -9x +14
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%2B2%29%2F%287-x%29%29%2F%28%28x%5E2-5x%2B6%29%2F%28x%5E2-9x%2B14%29%29 Start with the given expression.


%28%28x%2B2%29%2F%287-x%29%29%28%28x%5E2-9x%2B14%29%2F%28x%5E2-5x%2B6%29%29 Multiply the first fraction %28x%2B2%29%2F%287-x%29 by the reciprocal of the second fraction %28x%5E2-5x%2B6%29%2F%28x%5E2-9x%2B14%29.


%28%28%28x%2B2%29%29%2F%28-%28x-7%29%29%29%28%28x%5E2-9x%2B14%29%2F%28x%5E2-5x%2B6%29%29 Factor 7-x to get -%28x-7%29.


Factor x%5E2-9x%2B14 to get %28x-2%29%28x-7%29.


Factor x%5E2-5x%2B6 to get %28x-2%29%28x-3%29.


%28%28x%2B2%29%28x-2%29%2A%28x-7%29%29%2F%28-%28x-7%29%28x-2%29%28x-3%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


-%28x%2B2%29%2F%28x-3%29 Simplify.


So %28%28x%2B2%29%2F%287-x%29%29%2F%28%28x%5E2-5x%2B6%29%2F%28x%5E2-9x%2B14%29%29 simplifies to -%28x%2B2%29%2F%28x-3%29.


In other words,


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Jim