1/x^2-8=6/x

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Solution for 1/x^2-8=6/x 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/(x^2)-8 = 6/x // - 6/x

1/(x^2)-(6/x)-8 = 0

1/(x^2)-6*x^-1-8 = 0

x^-2-6*x^-1-8 = 0

t_1 = x^-1

1*t_1^2-6*t_1^1-8 = 0

t_1^2-6*t_1-8 = 0

DELTA = (-6)^2-(-8*1*4)

DELTA = 68

DELTA > 0

t_1 = (68^(1/2)+6)/(1*2) or t_1 = (6-68^(1/2))/(1*2)

t_1 = (2*17^(1/2)+6)/2 or t_1 = (6-2*17^(1/2))/2

t_1 = (6-2*17^(1/2))/2

x^-1-((6-2*17^(1/2))/2) = 0

1*x^-1 = (6-2*17^(1/2))/2 // : 1

x^-1 = (6-2*17^(1/2))/2

-1 < 0

1/(x^1) = (6-2*17^(1/2))/2 // * x^1

1 = ((6-2*17^(1/2))/2)*x^1 // : (6-2*17^(1/2))/2

2*(6-2*17^(1/2))^-1 = x^1

x = 2*(6-2*17^(1/2))^-1

t_1 = (2*17^(1/2)+6)/2

x^-1-((2*17^(1/2)+6)/2) = 0

1*x^-1 = (2*17^(1/2)+6)/2 // : 1

x^-1 = (2*17^(1/2)+6)/2

-1 < 0

1/(x^1) = (2*17^(1/2)+6)/2 // * x^1

1 = ((2*17^(1/2)+6)/2)*x^1 // : (2*17^(1/2)+6)/2

2*(2*17^(1/2)+6)^-1 = x^1

x = 2*(2*17^(1/2)+6)^-1

x in { 2*(6-2*17^(1/2))^-1, 2*(2*17^(1/2)+6)^-1 }

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