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

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


D( y )

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

y-1 = 0

y = 0

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

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

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

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

y^2+y-1 = 0

y^2+y-1 = 0

y^2+y-1 = 0

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

DELTA = 5

DELTA > 0

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

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

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

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

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

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

( y+(5^(1/2)+1)/2 )

y+(5^(1/2)+1)/2 = 0 // - (5^(1/2)+1)/2

y = -((5^(1/2)+1)/2)

( y-((5^(1/2)-1)/2) )

y-((5^(1/2)-1)/2) = 0 // + (5^(1/2)-1)/2

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

y-1 = 0

y-1 = 0

y-1 = 0 // + 1

y = 1

y = 0

y = 0

y in (-oo:-((5^(1/2)+1)/2)) U (-((5^(1/2)+1)/2):0) U (0:(5^(1/2)-1)/2) U ((5^(1/2)-1)/2:1) U (1:+oo)

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

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

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

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

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

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

y^2+3*y-6 = 0

y^2+3*y-6 = 0

y^2+3*y-6 = 0

DELTA = 3^2-(-6*1*4)

DELTA = 33

DELTA > 0

y = (33^(1/2)-3)/(1*2) or y = (-33^(1/2)-3)/(1*2)

y = (33^(1/2)-3)/2 or y = (-(33^(1/2)+3))/2

(y+(33^(1/2)+3)/2)*(y-((33^(1/2)-3)/2)) = 0

((y+(33^(1/2)+3)/2)*(y-((33^(1/2)-3)/2)))/(y*(y-1)) = 0

((y+(33^(1/2)+3)/2)*(y-((33^(1/2)-3)/2)))/(y*(y-1)) = 0 // * y*(y-1)

(y+(33^(1/2)+3)/2)*(y-((33^(1/2)-3)/2)) = 0

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

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

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

y^2+y-1 = 0

y^2+y-1 = 0

y^2+y-1 = 0

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

DELTA = 5

DELTA > 0

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

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

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

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

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

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

((y+(33^(1/2)+3)/2)*(y-((33^(1/2)-3)/2)))/((y+(5^(1/2)+1)/2)*(y-((5^(1/2)-1)/2))) = 0

( y+(33^(1/2)+3)/2 )

y+(33^(1/2)+3)/2 = 0 // - (33^(1/2)+3)/2

y = -((33^(1/2)+3)/2)

( y-((33^(1/2)-3)/2) )

y-((33^(1/2)-3)/2) = 0 // + (33^(1/2)-3)/2

y = (33^(1/2)-3)/2

y in { -((33^(1/2)+3)/2), (33^(1/2)-3)/2 }

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