SOLUTION: (13) Simplify: 20 + 7x - 3x^2 / x^2 - 16 (divided by) 6x + 10 / 2x^2 + 5x - 12 Thank you so much ! Really do Appreciate it alot

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (13) Simplify: 20 + 7x - 3x^2 / x^2 - 16 (divided by) 6x + 10 / 2x^2 + 5x - 12 Thank you so much ! Really do Appreciate it alot       Log On


   

Question 174833This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: (13) Simplify:
20 + 7x - 3x^2 / x^2 - 16 (divided by) 6x + 10 / 2x^2 + 5x - 12



Thank you so much ! Really do Appreciate it alot This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%2820%2B7x-3x%5E2%29%2F%28x%5E2-16%29%29%2F%28%286x%2B10%29%2F%282x%5E2%2B5x-12%29%29 Start with the given expression.


%28%28-3x%5E2%2B7x%2B20%29%2F%28x%5E2-16%29%29%2F%28%286x%2B10%29%2F%282x%5E2%2B5x-12%29%29 Rearrange the terms.


%28%28-3x%5E2%2B7x%2B20%29%2F%28x%5E2-16%29%29%28%282x%5E2%2B5x-12%29%2F%286x%2B10%29%29 Multiply the first fraction %28-3x%5E2%2B7x%2B20%29%2F%28x%5E2-16%29 by the reciprocal of the second fraction %286x%2B10%29%2F%282x%5E2%2B5x-12%29.


Factor -3x%5E2%2B7x%2B20 to get -%283x%2B5%29%28x-4%29.


Factor x%5E2-16 to get %28x-4%29%28x%2B4%29.


Factor 2x%5E2%2B5x-12 to get %28x%2B4%29%282x-3%29.


Factor 6x%2B10 to get 2%283x%2B5%29.


%28-%283x%2B5%29%28x-4%29%28x%2B4%29%282x-3%29%29%2F%282%28x-4%29%28x%2B4%29%283x%2B5%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


-%282x-3%29%2F%282%29 Simplify.



So %28%2820%2B7x-3x%5E2%29%2F%28x%5E2-16%29%29%2F%28%286x%2B10%29%2F%282x%5E2%2B5x-12%29%29 simplifies to -%282x-3%29%2F%282%29.