(8/x^2-16)-(1/x-4)=1

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Solution for (8/x^2-16)-(1/x-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)

8/(x^2)-(1/x)-16+4 = 1 // - 1

8/(x^2)-(1/x)-16-1+4 = 0

8/(x^2)-x^-1-16-1+4 = 0

8*x^-2-x^-1-13 = 0

t_1 = x^-1

8*t_1^2-1*t_1^1-13 = 0

8*t_1^2-t_1-13 = 0

DELTA = (-1)^2-(-13*4*8)

DELTA = 417

DELTA > 0

t_1 = (417^(1/2)+1)/(2*8) or t_1 = (1-417^(1/2))/(2*8)

t_1 = (417^(1/2)+1)/16 or t_1 = (1-417^(1/2))/16

t_1 = (1-417^(1/2))/16

x^-1-((1-417^(1/2))/16) = 0

1*x^-1 = (1-417^(1/2))/16 // : 1

x^-1 = (1-417^(1/2))/16

-1 < 0

1/(x^1) = (1-417^(1/2))/16 // * x^1

1 = ((1-417^(1/2))/16)*x^1 // : (1-417^(1/2))/16

16*(1-417^(1/2))^-1 = x^1

x = 16*(1-417^(1/2))^-1

t_1 = (417^(1/2)+1)/16

x^-1-((417^(1/2)+1)/16) = 0

1*x^-1 = (417^(1/2)+1)/16 // : 1

x^-1 = (417^(1/2)+1)/16

-1 < 0

1/(x^1) = (417^(1/2)+1)/16 // * x^1

1 = ((417^(1/2)+1)/16)*x^1 // : (417^(1/2)+1)/16

16*(417^(1/2)+1)^-1 = x^1

x = 16*(417^(1/2)+1)^-1

x in { 16*(1-417^(1/2))^-1, 16*(417^(1/2)+1)^-1 }

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