1-(1/x)=12/x^2

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Solution for 1-(1/x)=12/x^2 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) = 12/(x^2) // - 12/(x^2)

1-(1/x)-(12/(x^2)) = 0

1-x^-1-12*x^-2 = 0

t_1 = x^-1

1-12*t_1^2-1*t_1^1 = 0

1-12*t_1^2-t_1 = 0

DELTA = (-1)^2-(-12*1*4)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+1)/(-12*2) or t_1 = (1-49^(1/2))/(-12*2)

t_1 = -1/3 or t_1 = 1/4

t_1 = -1/3

x^-1+1/3 = 0

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

x^-1 = -1/3

-1 < 0

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

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

-3 = x^1

x = -3

t_1 = 1/4

x^-1-1/4 = 0

1*x^-1 = 1/4 // : 1

x^-1 = 1/4

-1 < 0

1/(x^1) = 1/4 // * x^1

1 = 1/4*x^1 // : 1/4

4 = x^1

x = 4

x in { -3, 4 }

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