SOLUTION: Divide 2x^2+5x-12/2x^2-7x+6 ___________ ________ 9x^2-16/3x^2-x-4

Algebra ->  Rational-functions -> SOLUTION: Divide 2x^2+5x-12/2x^2-7x+6 ___________ ________ 9x^2-16/3x^2-x-4      Log On


   

Question 118203: Divide
2x^2+5x-12/2x^2-7x+6
____________________
9x^2-16/3x^2-x-4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%282x%5E2%2B5x-12%29%2F%282x%5E2-7x%2B6%29%29%2F%28%289x%5E2-16%29%2F%283x%5E2-x-4%29%29 Start with the given expression

Multiply the first fraction by the reciprocal of the second fraction

Factor 2x%5E2%2B5x-12 to get %28x%2B4%29%282x-3%29

Factor 2x%5E2-7x%2B6 to get %28x-2%29%282x-3%29

Factor 3x%5E2-x-4 to get %283x-4%29%28x%2B1%29

Factor 9x%5E2-16 to get %283x%2B4%29%283x-4%29


%28x%2B4%29%282x-3%29%283x-4%29%28x%2B1%29%2F%28x-2%29%282x-3%29%283x%2B4%29%283x-4%29 Combine the fractions


Cancel like terms


%28x%2B4%29%28x%2B1%29%2F%28x-2%29%283x%2B4%29 Simplify


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Answer:

So %28%282x%5E2%2B5x-12%29%2F%282x%5E2-7x%2B6%29%29%2F%28%289x%5E2-16%29%2F%283x%5E2-x-4%29%29 simplifies to %28x%2B4%29%28x%2B1%29%2F%28x-2%29%283x%2B4%29. In other words