# Simplify ((y^2-4y-12)/(y^2-4y+4))÷((y-6)/(y-2)) y2-4y-12y2-4y+4÷y-6y-2
To divide by a fraction, multiply by its reciprocal.
y2-4y-12y2-4y+4⋅y-2y-6
Factor y2-4y-12 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -12 and whose sum is -4.
-6,2
Write the factored form using these integers.
(y-6)(y+2)y2-4y+4⋅y-2y-6
(y-6)(y+2)y2-4y+4⋅y-2y-6
Factor using the perfect square rule.
Rewrite 4 as 22.
(y-6)(y+2)y2-4y+22⋅y-2y-6
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-6)(y+2)(y-2)2⋅y-2y-6
(y-6)(y+2)(y-2)2⋅y-2y-6
Reduce the expression by cancelling the common factors.
Cancel the common factor of y-6.
Cancel the common factor.
(y-6)(y+2)(y-2)2⋅y-2y-6
Rewrite the expression.
y+2(y-2)2(y-2)
y+2(y-2)2(y-2)
Cancel the common factor of y-2.
Factor y-2 out of (y-2)2.
y+2(y-2)(y-2)(y-2)
Cancel the common factor.
y+2(y-2)(y-2)(y-2)
Rewrite the expression.
y+2y-2
y+2y-2
y+2y-2
Simplify ((y^2-4y-12)/(y^2-4y+4))÷((y-6)/(y-2))

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