SOLUTION: Divide and show steps 2x^2+5x-12 ---------- 9x^2-16 divided by 2x^2-7x+6 --------- 3x^2-x-4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Divide and show steps 2x^2+5x-12 ---------- 9x^2-16 divided by 2x^2-7x+6 --------- 3x^2-x-4       Log On


   

Question 183023: Divide and show steps
2x^2+5x-12
----------
9x^2-16
divided by
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%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.



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