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

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Solution for (x/x^2-9)+(3/x^2-9)=0 equation: 


D( x )

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

x^-1+3*x^-2-18 = 0

t_1 = x^-1

3*t_1^2+1*t_1^1-18 = 0

3*t_1^2+t_1-18 = 0

DELTA = 1^2-(-18*3*4)

DELTA = 217

DELTA > 0

t_1 = (217^(1/2)-1)/(2*3) or t_1 = (-217^(1/2)-1)/(2*3)

t_1 = (217^(1/2)-1)/6 or t_1 = (-(217^(1/2)+1))/6

t_1 = (-(217^(1/2)+1))/6

x^-1-((-(217^(1/2)+1))/6) = 0

x^-1+(1/6)*(217^(1/2)+1) = 0

1*x^-1 = -(1/6*(217^(1/2)+1)) // : 1

x^-1 = -1/6*(217^(1/2)+1)

-1 < 0

1/(x^1) = -1/6*(217^(1/2)+1) // * x^1

1 = -1/6*(217^(1/2)+1)*x^1 // : -1/6*(217^(1/2)+1)

-6*(217^(1/2)+1)^-1 = x^1

x = -6*(217^(1/2)+1)^-1

t_1 = (217^(1/2)-1)/6

x^-1-((217^(1/2)-1)/6) = 0

1*x^-1 = (217^(1/2)-1)/6 // : 1

x^-1 = (217^(1/2)-1)/6

-1 < 0

1/(x^1) = (217^(1/2)-1)/6 // * x^1

1 = ((217^(1/2)-1)/6)*x^1 // : (217^(1/2)-1)/6

6*(217^(1/2)-1)^-1 = x^1

x = 6*(217^(1/2)-1)^-1

x in { -6*(217^(1/2)+1)^-1, 6*(217^(1/2)-1)^-1 }

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