SOLUTION: (2x^2-12x+18) (2x^2+6x+4) over > multiplied by < over (4x^2-8x-12) (x^2 +6x+8)

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: (2x^2-12x+18) (2x^2+6x+4) over > multiplied by < over (4x^2-8x-12) (x^2 +6x+8)      Log On

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Question 171417This question is from textbook Algebra 2
: (2x^2-12x+18) (2x^2+6x+4)
over > multiplied by < over
(4x^2-8x-12) (x^2 +6x+8)This question is from textbook Algebra 2

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

%28%282x%5E2-12x%2B18%29%2F%284x%5E2-8x-12%29%29%28%282x%5E2%2B6x%2B4%29%2F%28x%5E2%2B6x%2B8%29%29 Start with the given expression.


%28%282%28x-3%29%28x-3%29%29%2F%284x%5E2-8x-12%29%29%28%282x%5E2%2B6x%2B4%29%2F%28x%5E2%2B6x%2B8%29%29 Factor 2x%5E2-12x%2B18 to get 2%28x-3%29%28x-3%29.


%28%282%28x-3%29%28x-3%29%29%2F%284%28x%2B1%29%28x-3%29%29%29%28%282x%5E2%2B6x%2B4%29%2F%28x%5E2%2B6x%2B8%29%29 Factor 4x%5E2-8x-12 to get 4%28x%2B1%29%28x-3%29.


%28%282%28x-3%29%28x-3%29%29%2F%284%28x%2B1%29%28x-3%29%29%29%28%282%28x%2B2%29%28x%2B1%29%29%2F%28x%5E2%2B6x%2B8%29%29 Factor 2x%5E2%2B6x%2B4 to get 2%28x%2B2%29%28x%2B1%29.


%28%282%28x-3%29%28x-3%29%29%2F%284%28x%2B1%29%28x-3%29%29%29%28%282%28x%2B2%29%28x%2B1%29%29%2F%28%28x%2B4%29%28x%2B2%29%29%29 Factor x%5E2%2B6x%2B8 to get %28x%2B4%29%28x%2B2%29.


%282%2A2%28x-3%29%28x-3%29%28x%2B2%29%28x%2B1%29%29%2F%284%28x%2B1%29%28x-3%29%28x%2B4%29%28x%2B2%29%29 Combine the fractions.


%282%2A2%2Ahighlight%28%28x-3%29%29%28x-3%29highlight%28%28x%2B2%29%29highlight%28%28x%2B1%29%29%29%2F%284%2Ahighlight%28%28x%2B1%29%29highlight%28%28x-3%29%29%28x%2B4%29highlight%28%28x%2B2%29%29%29 Highlight the common terms.


%282%2A2%2Across%28%28x-3%29%29%28x-3%29cross%28%28x%2B2%29%29cross%28%28x%2B1%29%29%29%2F%284%2Across%28%28x%2B1%29%29cross%28%28x-3%29%29%28x%2B4%29cross%28%28x%2B2%29%29%29 Cancel out the common terms.


%282%2A2%28x-3%29%29%2F%284%28x%2B4%29%29 Simplify.


%284%28x-3%29%29%2F%284%28x%2B4%29%29 Multiply


%28x-3%29%2F%28x%2B4%29 Reduce


So %28%282x%5E2-12x%2B18%29%2F%284x%5E2-8x-12%29%29%28%282x%5E2%2B6x%2B4%29%2F%28x%5E2%2B6x%2B8%29%29 simplifies to %28x-3%29%2F%28x%2B4%29.