2x/x-3-6/x=18/x^2-3

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Solution for 2x/x-3-6/x=18/x^2-3 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)

(2*x)/x-(6/x)-3 = 18/(x^2)-3 // - 18/(x^2)-3

(2*x)/x-(6/x)-(18/(x^2))-3+3 = 0

(2*x)/x-6*x^-1-18*x^-2-3+3 = 0

2-6*x^-1-18*x^-2 = 0

t_1 = x^-1

2-18*t_1^2-6*t_1^1 = 0

2-18*t_1^2-6*t_1 = 0

DELTA = (-6)^2-(-18*2*4)

DELTA = 180

DELTA > 0

t_1 = (180^(1/2)+6)/(-18*2) or t_1 = (6-180^(1/2))/(-18*2)

t_1 = (6*5^(1/2)+6)/(-36) or t_1 = (6-6*5^(1/2))/(-36)

t_1 = (6*5^(1/2)+6)/(-36)

x^-1-((6*5^(1/2)+6)/(-36)) = 0

1*x^-1 = (6*5^(1/2)+6)/(-36) // : 1

x^-1 = (6*5^(1/2)+6)/(-36)

-1 < 0

1/(x^1) = (6*5^(1/2)+6)/(-36) // * x^1

1 = ((6*5^(1/2)+6)/(-36))*x^1 // : (6*5^(1/2)+6)/(-36)

-36*(6*5^(1/2)+6)^-1 = x^1

x = -36*(6*5^(1/2)+6)^-1

t_1 = (6-6*5^(1/2))/(-36)

x^-1-((6-6*5^(1/2))/(-36)) = 0

1*x^-1 = (6-6*5^(1/2))/(-36) // : 1

x^-1 = (6-6*5^(1/2))/(-36)

-1 < 0

1/(x^1) = (6-6*5^(1/2))/(-36) // * x^1

1 = ((6-6*5^(1/2))/(-36))*x^1 // : (6-6*5^(1/2))/(-36)

-36*(6-6*5^(1/2))^-1 = x^1

x = -36*(6-6*5^(1/2))^-1

x in { -36*(6*5^(1/2)+6)^-1, -36*(6-6*5^(1/2))^-1 }

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