(6/x+3)-(2/x-3)=(5/x^2-9)

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Solution for (6/x+3)-(2/x-3)=(5/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)

6/x-(2/x)+3+3 = 5/(x^2)-9 // - 5/(x^2)-9

6/x-(2/x)-(5/(x^2))+3+3+9 = 0

6/x-2*x^-1-5*x^-2+3+3+9 = 0

4*x^-1-5*x^-2+15 = 0

t_1 = x^-1

4*t_1^1-5*t_1^2+15 = 0

4*t_1-5*t_1^2+15 = 0

DELTA = 4^2-(-5*4*15)

DELTA = 316

DELTA > 0

t_1 = (316^(1/2)-4)/(-5*2) or t_1 = (-316^(1/2)-4)/(-5*2)

t_1 = (2*79^(1/2)-4)/(-10) or t_1 = (-2*79^(1/2)-4)/(-10)

t_1 = (2*79^(1/2)-4)/(-10)

x^-1-((2*79^(1/2)-4)/(-10)) = 0

1*x^-1 = (2*79^(1/2)-4)/(-10) // : 1

x^-1 = (2*79^(1/2)-4)/(-10)

-1 < 0

1/(x^1) = (2*79^(1/2)-4)/(-10) // * x^1

1 = ((2*79^(1/2)-4)/(-10))*x^1 // : (2*79^(1/2)-4)/(-10)

-10*(2*79^(1/2)-4)^-1 = x^1

x = -10*(2*79^(1/2)-4)^-1

t_1 = (-2*79^(1/2)-4)/(-10)

x^-1-((-2*79^(1/2)-4)/(-10)) = 0

1*x^-1 = (-2*79^(1/2)-4)/(-10) // : 1

x^-1 = (-2*79^(1/2)-4)/(-10)

-1 < 0

1/(x^1) = (-2*79^(1/2)-4)/(-10) // * x^1

1 = ((-2*79^(1/2)-4)/(-10))*x^1 // : (-2*79^(1/2)-4)/(-10)

-10*(-2*79^(1/2)-4)^-1 = x^1

x = -10*(-2*79^(1/2)-4)^-1

x in { -10*(2*79^(1/2)-4)^-1, -10*(-2*79^(1/2)-4)^-1 }

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