4-1/x=3/x2

Solution for 4-1/x=3/x2 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)

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

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

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

t_1 = x^-1

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

4-3*t_1^2-t_1 = 0

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

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+1)/(-3*2) or t_1 = (1-49^(1/2))/(-3*2)

t_1 = -4/3 or t_1 = 1

t_1 = -4/3

x^-1+4/3 = 0

1*x^-1 = -4/3 // : 1

x^-1 = -4/3

-1 < 0

1/(x^1) = -4/3 // * x^1

1 = -4/3*x^1 // : -4/3

-3/4 = x^1

x = -3/4

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

x in { -3/4, 1 }