(3/x-1)+(6/x+1)=(2/x^2-1)

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Solution for (3/x-1)+(6/x+1)=(2/x^2-1) 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+6/x-1+1 = 2/(x^2)-1 // - 2/(x^2)-1

3/x+6/x-(2/(x^2))-1+1+1 = 0

3/x+6/x-2*x^-2-1+1+1 = 0

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

t_1 = x^-1

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

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

DELTA = 9^2-(-2*1*4)

DELTA = 89

DELTA > 0

t_1 = (89^(1/2)-9)/(-2*2) or t_1 = (-89^(1/2)-9)/(-2*2)

t_1 = (89^(1/2)-9)/(-4) or t_1 = (89^(1/2)+9)/4

t_1 = (89^(1/2)-9)/(-4)

x^-1-((89^(1/2)-9)/(-4)) = 0

1*x^-1 = (89^(1/2)-9)/(-4) // : 1

x^-1 = (89^(1/2)-9)/(-4)

-1 < 0

1/(x^1) = (89^(1/2)-9)/(-4) // * x^1

1 = ((89^(1/2)-9)/(-4))*x^1 // : (89^(1/2)-9)/(-4)

-4*(89^(1/2)-9)^-1 = x^1

x = -4*(89^(1/2)-9)^-1

t_1 = (89^(1/2)+9)/4

x^-1-((89^(1/2)+9)/4) = 0

1*x^-1 = (89^(1/2)+9)/4 // : 1

x^-1 = (89^(1/2)+9)/4

-1 < 0

1/(x^1) = (89^(1/2)+9)/4 // * x^1

1 = ((89^(1/2)+9)/4)*x^1 // : (89^(1/2)+9)/4

4*(89^(1/2)+9)^-1 = x^1

x = 4*(89^(1/2)+9)^-1

x in { -4*(89^(1/2)-9)^-1, 4*(89^(1/2)+9)^-1 }

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