(x/x-3)-(1/x+3)=6/x^2-9

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Solution for (x/x-3)-(1/x+3)=6/x^2-9 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)

x/x-(1/x)-3-3 = 6/(x^2)-9 // - 6/(x^2)-9

x/x-(1/x)-(6/(x^2))-3-3+9 = 0

x/x-x^-1-6*x^-2-3-3+9 = 0

4-x^-1-6*x^-2 = 0

t_1 = x^-1

4-6*t_1^2-1*t_1^1 = 0

4-6*t_1^2-t_1 = 0

DELTA = (-1)^2-(-6*4*4)

DELTA = 97

DELTA > 0

t_1 = (97^(1/2)+1)/(-6*2) or t_1 = (1-97^(1/2))/(-6*2)

t_1 = (97^(1/2)+1)/(-12) or t_1 = (1-97^(1/2))/(-12)

t_1 = (97^(1/2)+1)/(-12)

x^-1-((97^(1/2)+1)/(-12)) = 0

1*x^-1 = (97^(1/2)+1)/(-12) // : 1

x^-1 = (97^(1/2)+1)/(-12)

-1 < 0

1/(x^1) = (97^(1/2)+1)/(-12) // * x^1

1 = ((97^(1/2)+1)/(-12))*x^1 // : (97^(1/2)+1)/(-12)

-12*(97^(1/2)+1)^-1 = x^1

x = -12*(97^(1/2)+1)^-1

t_1 = (1-97^(1/2))/(-12)

x^-1-((1-97^(1/2))/(-12)) = 0

1*x^-1 = (1-97^(1/2))/(-12) // : 1

x^-1 = (1-97^(1/2))/(-12)

-1 < 0

1/(x^1) = (1-97^(1/2))/(-12) // * x^1

1 = ((1-97^(1/2))/(-12))*x^1 // : (1-97^(1/2))/(-12)

-12*(1-97^(1/2))^-1 = x^1

x = -12*(1-97^(1/2))^-1

x in { -12*(97^(1/2)+1)^-1, -12*(1-97^(1/2))^-1 }

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