1+3/x=2/x^2

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

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

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

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

t_1 = x^-1

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

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

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

DELTA = 17

DELTA > 0

t_1 = (17^(1/2)-3)/(-2*2) or t_1 = (-17^(1/2)-3)/(-2*2)

t_1 = (17^(1/2)-3)/(-4) or t_1 = (17^(1/2)+3)/4

t_1 = (17^(1/2)-3)/(-4)

x^-1-((17^(1/2)-3)/(-4)) = 0

1*x^-1 = (17^(1/2)-3)/(-4) // : 1

x^-1 = (17^(1/2)-3)/(-4)

-1 < 0

1/(x^1) = (17^(1/2)-3)/(-4) // * x^1

1 = ((17^(1/2)-3)/(-4))*x^1 // : (17^(1/2)-3)/(-4)

-4*(17^(1/2)-3)^-1 = x^1

x = -4*(17^(1/2)-3)^-1

t_1 = (17^(1/2)+3)/4

x^-1-((17^(1/2)+3)/4) = 0

1*x^-1 = (17^(1/2)+3)/4 // : 1

x^-1 = (17^(1/2)+3)/4

-1 < 0

1/(x^1) = (17^(1/2)+3)/4 // * x^1

1 = ((17^(1/2)+3)/4)*x^1 // : (17^(1/2)+3)/4

4*(17^(1/2)+3)^-1 = x^1

x = 4*(17^(1/2)+3)^-1

x in { -4*(17^(1/2)-3)^-1, 4*(17^(1/2)+3)^-1 }

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