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

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

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

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

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

t_1 = x^-1

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

3-2*t_1^2-t_1 = 0

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

DELTA = 25

DELTA > 0

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

t_1 = -3/2 or t_1 = 1

t_1 = -3/2

x^-1+3/2 = 0

1*x^-1 = -3/2 // : 1

x^-1 = -3/2

-1 < 0

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

1 = -3/2*x^1 // : -3/2

-2/3 = x^1

x = -2/3

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 { -2/3, 1 }