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

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

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

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

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

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

t_1 = x^-1

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

t_1-12*t_1^2+1 = 0

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

DELTA = 49

DELTA > 0

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

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

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

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

x in { -4, 3 }

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