1-3/x=4/x^2

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Solution for 1-3/x=4/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-(3/x) = 4/(x^2) // - 4/(x^2)

1-(3/x)-(4/(x^2)) = 0

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

t_1 = x^-1

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

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

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

DELTA = 25

DELTA > 0

t_1 = (25^(1/2)+3)/(-4*2) or t_1 = (3-25^(1/2))/(-4*2)

t_1 = -1 or t_1 = 1/4

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 = 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 { -1, 4 }

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