x/x-3+4/x+3=18/x^2-9

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Solution for x/x-3+4/x+3=18/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)

4/x+x/x-3+3 = 18/(x^2)-9 // - 18/(x^2)-9

4/x-(18/(x^2))+x/x-3+3+9 = 0

4/x-18*x^-2+x/x-3+3+9 = 0

4*x^-1-18*x^-2+10 = 0

t_1 = x^-1

4*t_1^1-18*t_1^2+10 = 0

4*t_1-18*t_1^2+10 = 0

DELTA = 4^2-(-18*4*10)

DELTA = 736

DELTA > 0

t_1 = (736^(1/2)-4)/(-18*2) or t_1 = (-736^(1/2)-4)/(-18*2)

t_1 = (4*46^(1/2)-4)/(-36) or t_1 = (-4*46^(1/2)-4)/(-36)

t_1 = (4*46^(1/2)-4)/(-36)

x^-1-((4*46^(1/2)-4)/(-36)) = 0

1*x^-1 = (4*46^(1/2)-4)/(-36) // : 1

x^-1 = (4*46^(1/2)-4)/(-36)

-1 < 0

1/(x^1) = (4*46^(1/2)-4)/(-36) // * x^1

1 = ((4*46^(1/2)-4)/(-36))*x^1 // : (4*46^(1/2)-4)/(-36)

-36*(4*46^(1/2)-4)^-1 = x^1

x = -36*(4*46^(1/2)-4)^-1

t_1 = (-4*46^(1/2)-4)/(-36)

x^-1-((-4*46^(1/2)-4)/(-36)) = 0

1*x^-1 = (-4*46^(1/2)-4)/(-36) // : 1

x^-1 = (-4*46^(1/2)-4)/(-36)

-1 < 0

1/(x^1) = (-4*46^(1/2)-4)/(-36) // * x^1

1 = ((-4*46^(1/2)-4)/(-36))*x^1 // : (-4*46^(1/2)-4)/(-36)

-36*(-4*46^(1/2)-4)^-1 = x^1

x = -36*(-4*46^(1/2)-4)^-1

x in { -36*(4*46^(1/2)-4)^-1, -36*(-4*46^(1/2)-4)^-1 }

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