1-5/x=-6/x^2

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Solution for 1-5/x=-6/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-(5/x) = -6/(x^2) // + -6/(x^2)

1-(5/x)-(-6/(x^2)) = 0

6*x^-2-5*x^-1+1 = 0

t_1 = x^-1

6*t_1^2-5*t_1^1+1 = 0

6*t_1^2-5*t_1+1 = 0

DELTA = (-5)^2-(1*4*6)

DELTA = 1

DELTA > 0

t_1 = (1^(1/2)+5)/(2*6) or t_1 = (5-1^(1/2))/(2*6)

t_1 = 1/2 or t_1 = 1/3

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 = 1/2

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

x in { 3, 2 }

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