Simplify (6y^2+11y+4)/(3y^2+7y+4)

Math
6y2+11y+43y2+7y+4
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=6⋅4=24 and whose sum is b=11.
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Factor 11 out of 11y.
6y2+11(y)+43y2+7y+4
Rewrite 11 as 3 plus 8
6y2+(3+8)y+43y2+7y+4
Apply the distributive property.
6y2+3y+8y+43y2+7y+4
6y2+3y+8y+43y2+7y+4
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(6y2+3y)+8y+43y2+7y+4
Factor out the greatest common factor (GCF) from each group.
3y(2y+1)+4(2y+1)3y2+7y+4
3y(2y+1)+4(2y+1)3y2+7y+4
Factor the polynomial by factoring out the greatest common factor, 2y+1.
(2y+1)(3y+4)3y2+7y+4
(2y+1)(3y+4)3y2+7y+4
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=3⋅4=12 and whose sum is b=7.
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Factor 7 out of 7y.
(2y+1)(3y+4)3y2+7(y)+4
Rewrite 7 as 3 plus 4
(2y+1)(3y+4)3y2+(3+4)y+4
Apply the distributive property.
(2y+1)(3y+4)3y2+3y+4y+4
(2y+1)(3y+4)3y2+3y+4y+4
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(2y+1)(3y+4)(3y2+3y)+4y+4
Factor out the greatest common factor (GCF) from each group.
(2y+1)(3y+4)3y(y+1)+4(y+1)
(2y+1)(3y+4)3y(y+1)+4(y+1)
Factor the polynomial by factoring out the greatest common factor, y+1.
(2y+1)(3y+4)(y+1)(3y+4)
(2y+1)(3y+4)(y+1)(3y+4)
Cancel the common factor of 3y+4.
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Cancel the common factor.
(2y+1)(3y+4)(y+1)(3y+4)
Rewrite the expression.
2y+1y+1
2y+1y+1
Simplify (6y^2+11y+4)/(3y^2+7y+4)

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