(2/x+2)+(15/x^2-4)=1

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Solution for (2/x+2)+(15/x^2-4)=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)

2/x+15/(x^2)-4+2 = 1 // - 1

2/x+15/(x^2)-4-1+2 = 0

2*x^-1+15*x^-2-3 = 0

t_1 = x^-1

15*t_1^2+2*t_1^1-3 = 0

15*t_1^2+2*t_1-3 = 0

DELTA = 2^2-(-3*4*15)

DELTA = 184

DELTA > 0

t_1 = (184^(1/2)-2)/(2*15) or t_1 = (-184^(1/2)-2)/(2*15)

t_1 = (2*46^(1/2)-2)/30 or t_1 = (-2*46^(1/2)-2)/30

t_1 = (-2*46^(1/2)-2)/30

x^-1-((-2*46^(1/2)-2)/30) = 0

1*x^-1 = (-2*46^(1/2)-2)/30 // : 1

x^-1 = (-2*46^(1/2)-2)/30

-1 < 0

1/(x^1) = (-2*46^(1/2)-2)/30 // * x^1

1 = ((-2*46^(1/2)-2)/30)*x^1 // : (-2*46^(1/2)-2)/30

30*(-2*46^(1/2)-2)^-1 = x^1

x = 30*(-2*46^(1/2)-2)^-1

t_1 = (2*46^(1/2)-2)/30

x^-1-((2*46^(1/2)-2)/30) = 0

1*x^-1 = (2*46^(1/2)-2)/30 // : 1

x^-1 = (2*46^(1/2)-2)/30

-1 < 0

1/(x^1) = (2*46^(1/2)-2)/30 // * x^1

1 = ((2*46^(1/2)-2)/30)*x^1 // : (2*46^(1/2)-2)/30

30*(2*46^(1/2)-2)^-1 = x^1

x = 30*(2*46^(1/2)-2)^-1

x in { 30*(-2*46^(1/2)-2)^-1, 30*(2*46^(1/2)-2)^-1 }

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