# Simplify (y^2-4y+4)/(3y^2-12)

y2-4y+43y2-12
Factor using the perfect square rule.
Rewrite 4 as 22.
y2-4y+223y2-12
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅y⋅-2
Simplify.
2ab=-4y
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=y and b=-2.
(y-2)23y2-12
(y-2)23y2-12
Simplify the denominator.
Factor 3 out of 3y2-12.
Factor 3 out of 3y2.
(y-2)23(y2)-12
Factor 3 out of -12.
(y-2)23y2+3⋅-4
Factor 3 out of 3y2+3⋅-4.
(y-2)23(y2-4)
(y-2)23(y2-4)
Rewrite 4 as 22.
(y-2)23(y2-22)
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=y and b=2.
(y-2)23(y+2)(y-2)
(y-2)23(y+2)(y-2)
Cancel the common factor of (y-2)2 and y-2.
Factor y-2 out of (y-2)2.
(y-2)(y-2)3(y+2)(y-2)
Cancel the common factors.
Factor y-2 out of 3(y+2)(y-2).
(y-2)(y-2)(y-2)(3(y+2))
Cancel the common factor.
(y-2)(y-2)(y-2)(3(y+2))
Rewrite the expression.
y-23(y+2)
y-23(y+2)
y-23(y+2)
Simplify (y^2-4y+4)/(3y^2-12)

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