SOLUTION: Would someone please help me with this. divide: 6x^2-x-12/9x^2-16 divided by 2x^2-7x+6/3x^2-x-4 Thanks ;)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Would someone please help me with this. divide: 6x^2-x-12/9x^2-16 divided by 2x^2-7x+6/3x^2-x-4 Thanks ;)      Log On


   

Question 178412: Would someone please help me with this.
divide:
6x^2-x-12/9x^2-16 divided by 2x^2-7x+6/3x^2-x-4
Thanks ;)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%286x%5E2-x-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%286x%5E2-x-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 %286x%5E2-x-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 6x%5E2-x-12 to get %283x%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.


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


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Answer:


So %28%286x%5E2-x-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%2B1%29%2F%28x-2%29.


In other words, where x%3C%3E-4%2F3, x%3C%3E4%2F3, x%3C%3E-3%2F2, x%3C%3E3%2F2, x%3C%3E2, or x%3C%3E-1.