(7/y+9)+(3/y-9)/(5/y-9)-(4/y+9)

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Solution for (7/y+9)+(3/y-9)/(5/y-9)-(4/y+9) equation: 


D( y )

y = 0

5/y-9 = 0

y = 0

y = 0

5/y-9 = 0

5/y-9 = 0

5*y^-1 = 9 // : 5

y^-1 = 9/5

-1 < 0

1/(y^1) = 9/5 // * y^1

1 = 9/5*y^1 // : 9/5

5/9 = y^1

y = 5/9

y in (-oo:0) U (0:5/9) U (5/9:+oo)

(3/y-9)/(5/y-9)+7/y-(4/y)-9+9 = 0

(3/y-9)/(5/y-9)+7/y-4*y^-1-9+9 = 0

(3*y^-1-9)/(5*y^-1-9)+7/y-4/y-9+9 = 0

(y*(3*y^-1-9))/(y*(5*y^-1-9))+(7*(5*y^-1-9))/(y*(5*y^-1-9))+(-4*(5*y^-1-9))/(y*(5*y^-1-9))+(-9*y*(5*y^-1-9))/(y*(5*y^-1-9))+(9*y*(5*y^-1-9))/(y*(5*y^-1-9)) = 0

y*(3*y^-1-9)+7*(5*y^-1-9)-4*(5*y^-1-9)-9*y*(5*y^-1-9)+9*y*(5*y^-1-9) = 0

81*y-9*y-81*y+35*y^-1-20*y^-1-60-45+36+45 = 0

81*y-9*y-81*y+15*y^-1-45-24+45 = 0

72*y-81*y+15*y^-1-69+45 = 0

15*y^-1-9*y-24 = 0

15*y^-1-9*y-24 = 0

3*(5*y^-1-3*y-8) = 0

5*y^-1-3*y^1-8*y^0 = 0

(5*y^0-3*y^2-8*y^1)/(y^1) = 0 // * y^2

y^1*(5*y^0-3*y^2-8*y^1) = 0

y^1

5-3*y^2-8*y = 0

5-3*y^2-8*y = 0

DELTA = (-8)^2-(-3*4*5)

DELTA = 124

DELTA > 0

y = (124^(1/2)+8)/(-3*2) or y = (8-124^(1/2))/(-3*2)

y = (2*31^(1/2)+8)/(-6) or y = (8-2*31^(1/2))/(-6)

y in { (2*31^(1/2)+8)/(-6), (8-2*31^(1/2))/(-6)} 

3*(y-((2*31^(1/2)+8)/(-6)))*(y-((8-2*31^(1/2))/(-6))) = 0

(3*(y-((2*31^(1/2)+8)/(-6)))*(y-((8-2*31^(1/2))/(-6))))/(y*(5*y^-1-9)) = 0

(3*(y-((2*31^(1/2)+8)/(-6)))*(y-((8-2*31^(1/2))/(-6))))/(y*(5*y^-1-9)) = 0 // * y*(5*y^-1-9)

3*(y-((2*31^(1/2)+8)/(-6)))*(y-((8-2*31^(1/2))/(-6))) = 0

( y-((2*31^(1/2)+8)/(-6)) )

y-((2*31^(1/2)+8)/(-6)) = 0 // + (2*31^(1/2)+8)/(-6)

y = (2*31^(1/2)+8)/(-6)

( y-((8-2*31^(1/2))/(-6)) )

y-((8-2*31^(1/2))/(-6)) = 0 // + (8-2*31^(1/2))/(-6)

y = (8-2*31^(1/2))/(-6)

y in { (2*31^(1/2)+8)/(-6), (8-2*31^(1/2))/(-6) }

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