(1/x-3)+(1/x+3)=(10/x^2-9)

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Solution for (1/x-3)+(1/x+3)=(10/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)

1/x+1/x-3+3 = 10/(x^2)-9 // - 10/(x^2)-9

1/x+1/x-(10/(x^2))-3+3+9 = 0

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

2*x^-1-10*x^-2+9 = 0

t_1 = x^-1

2*t_1^1-10*t_1^2+9 = 0

2*t_1-10*t_1^2+9 = 0

DELTA = 2^2-(-10*4*9)

DELTA = 364

DELTA > 0

t_1 = (364^(1/2)-2)/(-10*2) or t_1 = (-364^(1/2)-2)/(-10*2)

t_1 = (2*91^(1/2)-2)/(-20) or t_1 = (-2*91^(1/2)-2)/(-20)

t_1 = (2*91^(1/2)-2)/(-20)

x^-1-((2*91^(1/2)-2)/(-20)) = 0

1*x^-1 = (2*91^(1/2)-2)/(-20) // : 1

x^-1 = (2*91^(1/2)-2)/(-20)

-1 < 0

1/(x^1) = (2*91^(1/2)-2)/(-20) // * x^1

1 = ((2*91^(1/2)-2)/(-20))*x^1 // : (2*91^(1/2)-2)/(-20)

-20*(2*91^(1/2)-2)^-1 = x^1

x = -20*(2*91^(1/2)-2)^-1

t_1 = (-2*91^(1/2)-2)/(-20)

x^-1-((-2*91^(1/2)-2)/(-20)) = 0

1*x^-1 = (-2*91^(1/2)-2)/(-20) // : 1

x^-1 = (-2*91^(1/2)-2)/(-20)

-1 < 0

1/(x^1) = (-2*91^(1/2)-2)/(-20) // * x^1

1 = ((-2*91^(1/2)-2)/(-20))*x^1 // : (-2*91^(1/2)-2)/(-20)

-20*(-2*91^(1/2)-2)^-1 = x^1

x = -20*(-2*91^(1/2)-2)^-1

x in { -20*(2*91^(1/2)-2)^-1, -20*(-2*91^(1/2)-2)^-1 }

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