(1/x-2)+(x/x+2)=(5/x^2-4)

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Solution for (1/x-2)+(x/x+2)=(5/x^2-4) 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+x/x-2+2 = 5/(x^2)-4 // - 5/(x^2)-4

1/x-(5/(x^2))+x/x-2+2+4 = 0

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

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

t_1 = x^-1

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

t_1-5*t_1^2+5 = 0

DELTA = 1^2-(-5*4*5)

DELTA = 101

DELTA > 0

t_1 = (101^(1/2)-1)/(-5*2) or t_1 = (-101^(1/2)-1)/(-5*2)

t_1 = (101^(1/2)-1)/(-10) or t_1 = (101^(1/2)+1)/10

t_1 = (101^(1/2)-1)/(-10)

x^-1-((101^(1/2)-1)/(-10)) = 0

1*x^-1 = (101^(1/2)-1)/(-10) // : 1

x^-1 = (101^(1/2)-1)/(-10)

-1 < 0

1/(x^1) = (101^(1/2)-1)/(-10) // * x^1

1 = ((101^(1/2)-1)/(-10))*x^1 // : (101^(1/2)-1)/(-10)

-10*(101^(1/2)-1)^-1 = x^1

x = -10*(101^(1/2)-1)^-1

t_1 = (101^(1/2)+1)/10

x^-1-((101^(1/2)+1)/10) = 0

1*x^-1 = (101^(1/2)+1)/10 // : 1

x^-1 = (101^(1/2)+1)/10

-1 < 0

1/(x^1) = (101^(1/2)+1)/10 // * x^1

1 = ((101^(1/2)+1)/10)*x^1 // : (101^(1/2)+1)/10

10*(101^(1/2)+1)^-1 = x^1

x = 10*(101^(1/2)+1)^-1

x in { -10*(101^(1/2)-1)^-1, 10*(101^(1/2)+1)^-1 }

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