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

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
Write each expression with a common denominator of 2y, by multiplying each by an appropriate factor of 1.
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
Cancel the common factor of 2.
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)
Cancel the common factor of y-2 and 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)

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