1+1/x2=3/x

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

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

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

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

t_1 = x^-1

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

t_1^2-3*t_1+1 = 0

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

DELTA = 5

DELTA > 0

t_1 = (5^(1/2)+3)/(1*2) or t_1 = (3-5^(1/2))/(1*2)

t_1 = (5^(1/2)+3)/2 or t_1 = (3-5^(1/2))/2

t_1 = (3-5^(1/2))/2

x^-1-((3-5^(1/2))/2) = 0

1*x^-1 = (3-5^(1/2))/2 // : 1

x^-1 = (3-5^(1/2))/2

-1 < 0

1/(x^1) = (3-5^(1/2))/2 // * x^1

1 = ((3-5^(1/2))/2)*x^1 // : (3-5^(1/2))/2

2*(3-5^(1/2))^-1 = x^1

x = 2*(3-5^(1/2))^-1

t_1 = (5^(1/2)+3)/2

x^-1-((5^(1/2)+3)/2) = 0

1*x^-1 = (5^(1/2)+3)/2 // : 1

x^-1 = (5^(1/2)+3)/2

-1 < 0

1/(x^1) = (5^(1/2)+3)/2 // * x^1

1 = ((5^(1/2)+3)/2)*x^1 // : (5^(1/2)+3)/2

2*(5^(1/2)+3)^-1 = x^1

x = 2*(5^(1/2)+3)^-1

x in { 2*(3-5^(1/2))^-1, 2*(5^(1/2)+3)^-1 }

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