x/x-3-10/x+3=18/x^2-9

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Solution for x/x-3-10/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)

x/x-(10/x)-3+3 = 18/(x^2)-9 // - 18/(x^2)-9

x/x-(10/x)-(18/(x^2))-3+3+9 = 0

x/x-10*x^-1-18*x^-2-3+3+9 = 0

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

t_1 = x^-1

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

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

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

DELTA = 820

DELTA > 0

t_1 = (820^(1/2)+10)/(-18*2) or t_1 = (10-820^(1/2))/(-18*2)

t_1 = (2*205^(1/2)+10)/(-36) or t_1 = (10-2*205^(1/2))/(-36)

t_1 = (2*205^(1/2)+10)/(-36)

x^-1-((2*205^(1/2)+10)/(-36)) = 0

1*x^-1 = (2*205^(1/2)+10)/(-36) // : 1

x^-1 = (2*205^(1/2)+10)/(-36)

-1 < 0

1/(x^1) = (2*205^(1/2)+10)/(-36) // * x^1

1 = ((2*205^(1/2)+10)/(-36))*x^1 // : (2*205^(1/2)+10)/(-36)

-36*(2*205^(1/2)+10)^-1 = x^1

x = -36*(2*205^(1/2)+10)^-1

t_1 = (10-2*205^(1/2))/(-36)

x^-1-((10-2*205^(1/2))/(-36)) = 0

1*x^-1 = (10-2*205^(1/2))/(-36) // : 1

x^-1 = (10-2*205^(1/2))/(-36)

-1 < 0

1/(x^1) = (10-2*205^(1/2))/(-36) // * x^1

1 = ((10-2*205^(1/2))/(-36))*x^1 // : (10-2*205^(1/2))/(-36)

-36*(10-2*205^(1/2))^-1 = x^1

x = -36*(10-2*205^(1/2))^-1

x in { -36*(2*205^(1/2)+10)^-1, -36*(10-2*205^(1/2))^-1 }

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