1/x^2-2/x=3

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Solution for 1/x^2-2/x=3 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)-(2/x) = 3 // - 3

1/(x^2)-(2/x)-3 = 0

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

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

t_1 = x^-1

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

t_1^2-2*t_1-3 = 0

DELTA = (-2)^2-(-3*1*4)

DELTA = 16

DELTA > 0

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

t_1 = 3 or t_1 = -1

t_1 = -1

x^-1+1 = 0

1*x^-1 = -1 // : 1

x^-1 = -1

-1 < 0

1/(x^1) = -1 // * x^1

1 = -1*x^1 // : -1

-1 = x^1

x = -1

t_1 = 3

x^-1-3 = 0

1*x^-1 = 3 // : 1

x^-1 = 3

-1 < 0

1/(x^1) = 3 // * x^1

1 = 3*x^1 // : 3

1/3 = x^1

x = 1/3

x in { -1, 1/3 }

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