SOLUTION: Divide: 2x2 + 5x – 12 ÷ 2x2 – 7x + 6 9x2 – 16 3x2 – x – 4 Should be 2x^2+5x-12 over 9x^2-16/ 2x^2-7x+6 over 3x^2-x-4

Algebra ->  Radicals -> SOLUTION: Divide: 2x2 + 5x – 12 ÷ 2x2 – 7x + 6 9x2 – 16 3x2 – x – 4 Should be 2x^2+5x-12 over 9x^2-16/ 2x^2-7x+6 over 3x^2-x-4       Log On


   

Question 195791: Divide:
2x2 + 5x – 12 ÷ 2x2 – 7x + 6
9x2 – 16 3x2 – x – 4
Should be 2x^2+5x-12 over 9x^2-16/ 2x^2-7x+6 over 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%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%3E-1, x%3C%3E4%2F3, x%3C%3E3%2F2, or x%3C%3E2