4/x+7/x^2-2/x^3

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Solution for 4/x+7/x^2-2/x^3 equation: 


D( x )

x^3 = 0

x = 0

x^2 = 0

x^3 = 0

x^3 = 0

1*x^3 = 0 // : 1

x^3 = 0

x = 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)

4/x+7/(x^2)-(2/(x^3)) = 0

4/x+7/(x^2)-2*x^-3 = 0

4*x^-1+7*x^-2-2*x^-3 = 0

t_1 = x^-1

7*t_1^2-2*t_1^3+4*t_1^1 = 0

7*t_1^2-2*t_1^3+4*t_1 = 0

t_1*(7*t_1-2*t_1^2+4) = 0

7*t_1-2*t_1^2+4 = 0

DELTA = 7^2-(-2*4*4)

DELTA = 81

DELTA > 0

t_1 = (81^(1/2)-7)/(-2*2) or t_1 = (-81^(1/2)-7)/(-2*2)

t_1 = -1/2 or t_1 = 4

t_1 = 0

t_1 = 0

t_1 = -1/2

x^-1+1/2 = 0

1*x^-1 = -1/2 // : 1

x^-1 = -1/2

-1 < 0

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

1 = -1/2*x^1 // : -1/2

-2 = x^1

x = -2

t_1 = 4

x^-1-4 = 0

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

x^-1 = 4

-1 < 0

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

1 = 4*x^1 // : 4

1/4 = x^1

x = 1/4

t_1 = 0

x^-1+0 = 0

x^-1 = 0

1*x^-1 = 0 // : 1

x^-1 = 0

x naleu017Cy do O

x in { -2, 1/4 }

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