SOLUTION: Simplify the expression 12a^2+26a+12 / 6-5a-6a^2 A) 2(6a^2+13a+6) / -(6a^2+5a-5) B)-2 C)-2(3a+2) / (3a-2) D) 2(3a+2) / (3a-2)

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Simplify the expression 12a^2+26a+12 / 6-5a-6a^2 A) 2(6a^2+13a+6) / -(6a^2+5a-5) B)-2 C)-2(3a+2) / (3a-2) D) 2(3a+2) / (3a-2)      Log On

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Question 145589: Simplify the expression
12a^2+26a+12 / 6-5a-6a^2
A) 2(6a^2+13a+6) / -(6a^2+5a-5)
B)-2
C)-2(3a+2) / (3a-2)
D) 2(3a+2) / (3a-2)
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

%2812a%5E2%2B26a%2B12%29%2F%286-5a-6a%5E2%29 Start with the given expression.


%282%2A%282%2Aa%2B3%29%2A%283%2Aa%2B2%29%29%2F%286-5a-6a%5E2%29 Factor 12a%5E2%2B26a%2B12 to get 2%2A%282%2Aa%2B3%29%2A%283%2Aa%2B2%29.


%282%2A%282%2Aa%2B3%29%2A%283%2Aa%2B2%29%29%2F%28-%282%2Aa%2B3%29%2A%283%2Aa-2%29%29 Factor 6-5a-6a%5E2 to get -%282%2Aa%2B3%29%2A%283%2Aa-2%29.


-%28%282%29highlight%282%2Aa%2B3%29%283%2Aa%2B2%29%29%2F%28highlight%282%2Aa%2B3%29%283%2Aa-2%29%29 Highlight the common terms.


-%28%282%29cross%282%2Aa%2B3%29%283%2Aa%2B2%29%29%2F%28cross%282%2Aa%2B3%29%283%2Aa-2%29%29 Cancel out the common terms.


-%282%283%2Aa%2B2%29%29%2F%28%283%2Aa-2%29%29 Simplify.


So %2812a%5E2%2B26a%2B12%29%2F%286-5a-6a%5E2%29 simplifies to -%282%283%2Aa%2B2%29%29%2F%28%283%2Aa-2%29%29.


In other words, %2812a%5E2%2B26a%2B12%29%2F%286-5a-6a%5E2%29=-%282%283%2Aa%2B2%29%29%2F%28%283%2Aa-2%29%29 where a%3C%3E-3%2F2 or a%3C%3E2%2F3


So the answer is choice C