12-1y2-y2

Multiply the numerator by the reciprocal of the denominator.

(12-1y)22-y

To write 12 as a fraction with a common denominator, multiply by yy.

(12⋅yy-1y)22-y

To write -1y as a fraction with a common denominator, multiply by 22.

(12⋅yy-1y⋅22)22-y

Multiply 12 and yy.

(y2y-1y⋅22)22-y

Multiply 1y and 22.

(y2y-2y⋅2)22-y

Reorder the factors of y⋅2.

(y2y-22y)22-y

(y2y-22y)22-y

Combine the numerators over the common denominator.

y-22y⋅22-y

Factor 2 out of 2y.

y-22(y)⋅22-y

Cancel the common factor.

y-22y⋅22-y

Rewrite the expression.

y-2y⋅12-y

y-2y⋅12-y

Multiply y-2y and 12-y.

y-2y(2-y)

Factor -1 out of y.

-1(-y)-2y(2-y)

Rewrite -2 as -1(2).

-1(-y)-1(2)y(2-y)

Factor -1 out of -1(-y)-1(2).

-1(-y+2)y(2-y)

Reorder terms.

-1(-y+2)y(-y+2)

Cancel the common factor.

-1(-y+2)y(-y+2)

Rewrite the expression.

-1y

-1y

Move the negative in front of the fraction.

-1y

Simplify (1/2-1/y)/((2-y)/2)