8/y+3-2/y-3=12/y^2-9

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Solution for 8/y+3-2/y-3=12/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)

8/y-(2/y)-3+3 = 12/(y^2)-9 // - 12/(y^2)-9

8/y-(2/y)-(12/(y^2))-3+3+9 = 0

8/y-2*y^-1-12*y^-2-3+3+9 = 0

6*y^-1-12*y^-2+9 = 0

t_1 = y^-1

6*t_1^1-12*t_1^2+9 = 0

6*t_1-12*t_1^2+9 = 0

DELTA = 6^2-(-12*4*9)

DELTA = 468

DELTA > 0

t_1 = (468^(1/2)-6)/(-12*2) or t_1 = (-468^(1/2)-6)/(-12*2)

t_1 = (6*13^(1/2)-6)/(-24) or t_1 = (-6*13^(1/2)-6)/(-24)

t_1 = (6*13^(1/2)-6)/(-24)

y^-1-((6*13^(1/2)-6)/(-24)) = 0

1*y^-1 = (6*13^(1/2)-6)/(-24) // : 1

y^-1 = (6*13^(1/2)-6)/(-24)

-1 < 0

1/(y^1) = (6*13^(1/2)-6)/(-24) // * y^1

1 = ((6*13^(1/2)-6)/(-24))*y^1 // : (6*13^(1/2)-6)/(-24)

-24*(6*13^(1/2)-6)^-1 = y^1

y = -24*(6*13^(1/2)-6)^-1

t_1 = (-6*13^(1/2)-6)/(-24)

y^-1-((-6*13^(1/2)-6)/(-24)) = 0

1*y^-1 = (-6*13^(1/2)-6)/(-24) // : 1

y^-1 = (-6*13^(1/2)-6)/(-24)

-1 < 0

1/(y^1) = (-6*13^(1/2)-6)/(-24) // * y^1

1 = ((-6*13^(1/2)-6)/(-24))*y^1 // : (-6*13^(1/2)-6)/(-24)

-24*(-6*13^(1/2)-6)^-1 = y^1

y = -24*(-6*13^(1/2)-6)^-1

y in { -24*(6*13^(1/2)-6)^-1, -24*(-6*13^(1/2)-6)^-1 }

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