SOLUTION: . Divide: 6x^2 - x - 12/9x^2 – 16 ÷ 2x^2 – 7x + 6/3x^2 – x – 4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: . Divide: 6x^2 - x - 12/9x^2 – 16 ÷ 2x^2 – 7x + 6/3x^2 – x – 4       Log On


   

Question 167723: . Divide:
6x^2 - x - 12/9x^2 – 16 ÷ 2x^2 – 7x + 6/3x^2 – x – 4


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.


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.