(y-1)/(y+5)=(y-6)/(y+6)+1

Solution for (y-1)/(y+5)=(y-6)/(y+6)+1 equation:

D( y )

y+6 = 0

y+5 = 0

y+6 = 0

y+6 = 0

y+6 = 0 // - 6

y = -6

y+5 = 0

y+5 = 0

y+5 = 0 // - 5

y = -5

y in (-oo:-6) U (-6:-5) U (-5:+oo)

(y-1)/(y+5) = (y-6)/(y+6)+1 // - (y-6)/(y+6)+1

(y-1)/(y+5)-((y-6)/(y+6))-1 = 0

(y-1)/(y+5)+(-1*(y-6))/(y+6)-1 = 0

((y-1)*(y+6))/((y+5)*(y+6))+(-1*(y-6)*(y+5))/((y+5)*(y+6))+(-1*(y+5)*(y+6))/((y+5)*(y+6)) = 0

(y-1)*(y+6)-1*(y-6)*(y+5)-1*(y+5)*(y+6) = 0

6*y-y^2-11*y-30+24 = 0

-y^2-5*y-6 = 0

-y^2-5*y-6 = 0

-1*(y^2+5*y+6) = 0

y^2+5*y+6 = 0

DELTA = 5^2-(1*4*6)

DELTA = 1

DELTA > 0

y = (1^(1/2)-5)/(1*2) or y = (-1^(1/2)-5)/(1*2)

y = -2 or y = -3

-1*(y+3)*(y+2) = 0

(-1*(y+3)*(y+2))/((y+5)*(y+6)) = 0

(-1*(y+3)*(y+2))/((y+5)*(y+6)) = 0 // * (y+5)*(y+6)

-1*(y+3)*(y+2) = 0

( y+2 )

y+2 = 0 // - 2

y = -2

( y+3 )

y+3 = 0 // - 3

y = -3

y in { -2, -3 }