1-1/x-3=18/x^2-9

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Solution for 1-1/x-3=18/x^2-9 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)

1-(1/x)-3 = 18/(x^2)-9 // - 18/(x^2)-9

1-(1/x)-(18/(x^2))-3+9 = 0

1-x^-1-18*x^-2-3+9 = 0

7-x^-1-18*x^-2 = 0

t_1 = x^-1

7-18*t_1^2-1*t_1^1 = 0

7-18*t_1^2-t_1 = 0

DELTA = (-1)^2-(-18*4*7)

DELTA = 505

DELTA > 0

t_1 = (505^(1/2)+1)/(-18*2) or t_1 = (1-505^(1/2))/(-18*2)

t_1 = (505^(1/2)+1)/(-36) or t_1 = (1-505^(1/2))/(-36)

t_1 = (505^(1/2)+1)/(-36)

x^-1-((505^(1/2)+1)/(-36)) = 0

1*x^-1 = (505^(1/2)+1)/(-36) // : 1

x^-1 = (505^(1/2)+1)/(-36)

-1 < 0

1/(x^1) = (505^(1/2)+1)/(-36) // * x^1

1 = ((505^(1/2)+1)/(-36))*x^1 // : (505^(1/2)+1)/(-36)

-36*(505^(1/2)+1)^-1 = x^1

x = -36*(505^(1/2)+1)^-1

t_1 = (1-505^(1/2))/(-36)

x^-1-((1-505^(1/2))/(-36)) = 0

1*x^-1 = (1-505^(1/2))/(-36) // : 1

x^-1 = (1-505^(1/2))/(-36)

-1 < 0

1/(x^1) = (1-505^(1/2))/(-36) // * x^1

1 = ((1-505^(1/2))/(-36))*x^1 // : (1-505^(1/2))/(-36)

-36*(1-505^(1/2))^-1 = x^1

x = -36*(1-505^(1/2))^-1

x in { -36*(505^(1/2)+1)^-1, -36*(1-505^(1/2))^-1 }

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