5/y-3+1=30/y^2-9

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Solution for 5/y-3+1=30/y^2-9 equation: 


D( y )

y = 0

y^2 = 0

y = 0

y = 0

y^2 = 0

y^2 = 0

1*y^2 = 0 // : 1

y^2 = 0

y = 0

y in (-oo:0) U (0:+oo)

5/y-3+1 = 30/(y^2)-9 // - 30/(y^2)-9

5/y-(30/(y^2))-3+1+9 = 0

5/y-30*y^-2-3+1+9 = 0

5*y^-1-30*y^-2+7 = 0

t_1 = y^-1

5*t_1^1-30*t_1^2+7 = 0

5*t_1-30*t_1^2+7 = 0

DELTA = 5^2-(-30*4*7)

DELTA = 865

DELTA > 0

t_1 = (865^(1/2)-5)/(-30*2) or t_1 = (-865^(1/2)-5)/(-30*2)

t_1 = (865^(1/2)-5)/(-60) or t_1 = (865^(1/2)+5)/60

t_1 = (865^(1/2)-5)/(-60)

y^-1-((865^(1/2)-5)/(-60)) = 0

1*y^-1 = (865^(1/2)-5)/(-60) // : 1

y^-1 = (865^(1/2)-5)/(-60)

-1 < 0

1/(y^1) = (865^(1/2)-5)/(-60) // * y^1

1 = ((865^(1/2)-5)/(-60))*y^1 // : (865^(1/2)-5)/(-60)

-60*(865^(1/2)-5)^-1 = y^1

y = -60*(865^(1/2)-5)^-1

t_1 = (865^(1/2)+5)/60

y^-1-((865^(1/2)+5)/60) = 0

1*y^-1 = (865^(1/2)+5)/60 // : 1

y^-1 = (865^(1/2)+5)/60

-1 < 0

1/(y^1) = (865^(1/2)+5)/60 // * y^1

1 = ((865^(1/2)+5)/60)*y^1 // : (865^(1/2)+5)/60

60*(865^(1/2)+5)^-1 = y^1

y = 60*(865^(1/2)+5)^-1

y in { -60*(865^(1/2)-5)^-1, 60*(865^(1/2)+5)^-1 }

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