4/x+2+1/x-2=19/x^2-4

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Solution for 4/x+2+1/x-2=19/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)

4/x+1/x-2+2 = 19/(x^2)-4 // - 19/(x^2)-4

4/x+1/x-(19/(x^2))-2+2+4 = 0

4/x+1/x-19*x^-2-2+2+4 = 0

5*x^-1-19*x^-2+4 = 0

t_1 = x^-1

5*t_1^1-19*t_1^2+4 = 0

5*t_1-19*t_1^2+4 = 0

DELTA = 5^2-(-19*4*4)

DELTA = 329

DELTA > 0

t_1 = (329^(1/2)-5)/(-19*2) or t_1 = (-329^(1/2)-5)/(-19*2)

t_1 = (329^(1/2)-5)/(-38) or t_1 = (329^(1/2)+5)/38

t_1 = (329^(1/2)-5)/(-38)

x^-1-((329^(1/2)-5)/(-38)) = 0

1*x^-1 = (329^(1/2)-5)/(-38) // : 1

x^-1 = (329^(1/2)-5)/(-38)

-1 < 0

1/(x^1) = (329^(1/2)-5)/(-38) // * x^1

1 = ((329^(1/2)-5)/(-38))*x^1 // : (329^(1/2)-5)/(-38)

-38*(329^(1/2)-5)^-1 = x^1

x = -38*(329^(1/2)-5)^-1

t_1 = (329^(1/2)+5)/38

x^-1-((329^(1/2)+5)/38) = 0

1*x^-1 = (329^(1/2)+5)/38 // : 1

x^-1 = (329^(1/2)+5)/38

-1 < 0

1/(x^1) = (329^(1/2)+5)/38 // * x^1

1 = ((329^(1/2)+5)/38)*x^1 // : (329^(1/2)+5)/38

38*(329^(1/2)+5)^-1 = x^1

x = 38*(329^(1/2)+5)^-1

x in { -38*(329^(1/2)-5)^-1, 38*(329^(1/2)+5)^-1 }

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