1y-2+1y

To write 1y-2 as a fraction with a common denominator, multiply by yy.

1y-2⋅yy+1y

To write 1y as a fraction with a common denominator, multiply by y-2y-2.

1y-2⋅yy+1y⋅y-2y-2

Multiply 1y-2 and yy.

y(y-2)y+1y⋅y-2y-2

Multiply 1y and y-2y-2.

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

Reorder the factors of (y-2)y.

yy(y-2)+y-2y(y-2)

yy(y-2)+y-2y(y-2)

Combine the numerators over the common denominator.

y+y-2y(y-2)

Add y and y.

2y-2y(y-2)

Factor 2 out of 2y-2.

Factor 2 out of 2y.

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

Factor 2 out of -2.

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

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

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

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

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

Combine 1/(y-2)+1/y