Simplify (12a^2-3)/(6a^2-3a-3)

Math
12a2-36a2-3a-3
Cancel the common factor of 12a2-3 and 6a2-3a-3.
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Factor 3 out of 12a2.
3(4a2)-36a2-3a-3
Factor 3 out of -3.
3(4a2)+3(-1)6a2-3a-3
Factor 3 out of 3(4a2)+3(-1).
3(4a2-1)6a2-3a-3
Cancel the common factors.
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Factor 3 out of 6a2.
3(4a2-1)3(2a2)-3a-3
Factor 3 out of -3a.
3(4a2-1)3(2a2)+3(-a)-3
Factor 3 out of 3(2a2)+3(-a).
3(4a2-1)3(2a2-a)-3
Factor 3 out of -3.
3(4a2-1)3(2a2-a)+3(-1)
Factor 3 out of 3(2a2-a)+3(-1).
3(4a2-1)3(2a2-a-1)
Cancel the common factor.
3(4a2-1)3(2a2-a-1)
Rewrite the expression.
4a2-12a2-a-1
4a2-12a2-a-1
4a2-12a2-a-1
Simplify the numerator.
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Rewrite 4a2 as (2a)2.
(2a)2-12a2-a-1
Rewrite 1 as 12.
(2a)2-122a2-a-1
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=2a and b=1.
(2a+1)(2a-1)2a2-a-1
(2a+1)(2a-1)2a2-a-1
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅-1=-2 and whose sum is b=-1.
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Factor -1 out of -a.
(2a+1)(2a-1)2a2-(a)-1
Rewrite -1 as 1 plus -2
(2a+1)(2a-1)2a2+(1-2)a-1
Apply the distributive property.
(2a+1)(2a-1)2a2+1a-2a-1
Multiply a by 1.
(2a+1)(2a-1)2a2+a-2a-1
(2a+1)(2a-1)2a2+a-2a-1
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(2a+1)(2a-1)(2a2+a)-2a-1
Factor out the greatest common factor (GCF) from each group.
(2a+1)(2a-1)a(2a+1)-(2a+1)
(2a+1)(2a-1)a(2a+1)-(2a+1)
Factor the polynomial by factoring out the greatest common factor, 2a+1.
(2a+1)(2a-1)(2a+1)(a-1)
(2a+1)(2a-1)(2a+1)(a-1)
Cancel the common factor of 2a+1.
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Cancel the common factor.
(2a+1)(2a-1)(2a+1)(a-1)
Rewrite the expression.
2a-1a-1
2a-1a-1
Simplify (12a^2-3)/(6a^2-3a-3)

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