SOLUTION: Divide: [(2x^2 + 5x -12)/(9x^2 - 16)]/[(2x^2 - 7x + 6)/3x^2 - x - 4)] Any help will be appreciated. Thanks

Algebra ->  Rational-functions -> SOLUTION: Divide: [(2x^2 + 5x -12)/(9x^2 - 16)]/[(2x^2 - 7x + 6)/3x^2 - x - 4)] Any help will be appreciated. Thanks      Log On


   

Question 195959: Divide:
[(2x^2 + 5x -12)/(9x^2 - 16)]/[(2x^2 - 7x + 6)/3x^2 - x - 4)]
Any help will be appreciated. Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%282x%5E2%2B5x-12%29%2F%289x%5E2-16%29%29%2F%28%282x%5E2-7x%2B6%29%2F%283x%5E2-x-4%29%29 Start with the given expression.


%28%282x%5E2%2B5x-12%29%2F%289x%5E2-16%29%29%28%283x%5E2-x-4%29%2F%282x%5E2-7x%2B6%29%29 Multiply the first fraction %282x%5E2%2B5x-12%29%2F%289x%5E2-16%29 by the reciprocal of the second fraction %282x%5E2-7x%2B6%29%2F%283x%5E2-x-4%29.


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


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


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


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


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


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


%28x%5E2%2B5x%2B4%29%2F%283x%5E2-2x-8%29 FOIL


So %28%282x%5E2%2B5x-12%29%2F%289x%5E2-16%29%29%2F%28%282x%5E2-7x%2B6%29%2F%283x%5E2-x-4%29%29 simplifies to %28x%5E2%2B5x%2B4%29%2F%283x%5E2-2x-8%29.


In other words, where x%3C%3E-4%2F3, x%3C%3E4%2F3, x%3C%3E3%2F2, or x%3C%3E2