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

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

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

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))