SOLUTION: Simplify the rational expression. Assume that no denominator equals zero. 9-4x^2 over 6x^2-5x-6

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Question 412889: Simplify the rational expression. Assume that no denominator equals zero.
9-4x^2 over 6x^2-5x-6
Found 2 solutions by mananth, lwsshak3:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
9-4x^2 over 6x^2-5x-6
%289-4x%5E2%29%2F%286x%5E2-5x-6%29
%28%283%2B2x%29%283-2x%29%29%2F%286x%5E2-9x%2B4x-6%29
%28%283%2B2x%29%283-2x%29%29%2F%28%283x%282x-3%29%2B2%282x-3%29%29%29
%28%283%2B2x%29%283-2x%29%29%2F%28%283x%2B2%29%282x-3%29%29
%28-1%283%2B2x%29%28cross%282x-3%29%29%29%2F%28%283x%2B2%29%28cross%282x-3%29%29%29
%28-1%283%2B2x%29%29%2F%283x%2B2%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
9-4x^2 over 6x^2-5x-6
..
9-4x^2 = (3+2x)(3-2x) difference of two squares
6x^2-5x-6=(3x+2)(2x-3) factored form
=-(3x+2)(3-2x)
..
(9-4x^2)/(6x^2-5x-6)
=(3+2x)(3-2x)/-(3x+2)(3-2x)
=-(3+2x)/(3x+2)