(9/x-1)+1=(18/x^2-1)

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Solution for (9/x-1)+1=(18/x^2-1) equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

9/x-1+1 = 18/(x^2)-1 // - 18/(x^2)-1

9/x-(18/(x^2))-1+1+1 = 0

9/x-18*x^-2-1+1+1 = 0

9*x^-1-18*x^-2+1 = 0

t_1 = x^-1

9*t_1^1-18*t_1^2+1 = 0

9*t_1-18*t_1^2+1 = 0

DELTA = 9^2-(-18*1*4)

DELTA = 153

DELTA > 0

t_1 = (153^(1/2)-9)/(-18*2) or t_1 = (-153^(1/2)-9)/(-18*2)

t_1 = (3*17^(1/2)-9)/(-36) or t_1 = (-3*17^(1/2)-9)/(-36)

t_1 = (3*17^(1/2)-9)/(-36)

x^-1-((3*17^(1/2)-9)/(-36)) = 0

1*x^-1 = (3*17^(1/2)-9)/(-36) // : 1

x^-1 = (3*17^(1/2)-9)/(-36)

-1 < 0

1/(x^1) = (3*17^(1/2)-9)/(-36) // * x^1

1 = ((3*17^(1/2)-9)/(-36))*x^1 // : (3*17^(1/2)-9)/(-36)

-36*(3*17^(1/2)-9)^-1 = x^1

x = -36*(3*17^(1/2)-9)^-1

t_1 = (-3*17^(1/2)-9)/(-36)

x^-1-((-3*17^(1/2)-9)/(-36)) = 0

1*x^-1 = (-3*17^(1/2)-9)/(-36) // : 1

x^-1 = (-3*17^(1/2)-9)/(-36)

-1 < 0

1/(x^1) = (-3*17^(1/2)-9)/(-36) // * x^1

1 = ((-3*17^(1/2)-9)/(-36))*x^1 // : (-3*17^(1/2)-9)/(-36)

-36*(-3*17^(1/2)-9)^-1 = x^1

x = -36*(-3*17^(1/2)-9)^-1

x in { -36*(3*17^(1/2)-9)^-1, -36*(-3*17^(1/2)-9)^-1 }

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