1/(y-2)-1/(y-1)=1/6

Solution for 1/(y-2)-1/(y-1)=1/6 equation:

D( y )

y-1 = 0

y-2 = 0

y-1 = 0

y-1 = 0

y-1 = 0 // + 1

y = 1

y-2 = 0

y-2 = 0

y-2 = 0 // + 2

y = 2

y in (-oo:1) U (1:2) U (2:+oo)

1/(y-2)-(1/(y-1)) = 1/6 // - 1/6

1/(y-2)-(1/(y-1))-(1/6) = 0

1/(y-2)-(y-1)^-1-1/6 = 0

1/(y-2)-1/(y-1)-1/6 = 0

(1*6*(y-1))/(6*(y-2)*(y-1))+(-1*6*(y-2))/(6*(y-2)*(y-1))+(-1*(y-2)*(y-1))/(6*(y-2)*(y-1)) = 0

1*6*(y-1)-1*6*(y-2)-1*(y-2)*(y-1) = 0

3*y-y^2-2+6 = 0

3*y-y^2+4 = 0

3*y-y^2+4 = 0

3*y-y^2+4 = 0

DELTA = 3^2-(-1*4*4)

DELTA = 25

DELTA > 0

y = (25^(1/2)-3)/(-1*2) or y = (-25^(1/2)-3)/(-1*2)

y = -1 or y = 4

(y+1)*(y-4) = 0

((y+1)*(y-4))/(6*(y-2)*(y-1)) = 0

((y+1)*(y-4))/(6*(y-2)*(y-1)) = 0 // * 6*(y-2)*(y-1)

(y+1)*(y-4) = 0

( y+1 )

y+1 = 0 // - 1

y = -1

( y-4 )

y-4 = 0 // + 4

y = 4

y in { -1, 4 }