2+1/x=3/x^2

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

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

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

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

t_1 = x^-1

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

t_1-3*t_1^2+2 = 0

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

DELTA = 25

DELTA > 0

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

t_1 = -2/3 or t_1 = 1

t_1 = -2/3

x^-1+2/3 = 0

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

x^-1 = -2/3

-1 < 0

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

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

-3/2 = x^1

x = -3/2

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 { -3/2, 1 }

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