4/x-2+1/x+2=26/x2-4

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Solution for 4/x-2+1/x+2=26/x2-4 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 = 26/(x^2)-4 // - 26/(x^2)-4

4/x+1/x-(26/(x^2))-2+2+4 = 0

4/x+1/x-26*x^-2-2+2+4 = 0

5*x^-1-26*x^-2+4 = 0

t_1 = x^-1

5*t_1^1-26*t_1^2+4 = 0

5*t_1-26*t_1^2+4 = 0

DELTA = 5^2-(-26*4*4)

DELTA = 441

DELTA > 0

t_1 = (441^(1/2)-5)/(-26*2) or t_1 = (-441^(1/2)-5)/(-26*2)

t_1 = -4/13 or t_1 = 1/2

t_1 = -4/13

x^-1+4/13 = 0

1*x^-1 = -4/13 // : 1

x^-1 = -4/13

-1 < 0

1/(x^1) = -4/13 // * x^1

1 = -4/13*x^1 // : -4/13

-13/4 = x^1

x = -13/4

t_1 = 1/2

x^-1-1/2 = 0

1*x^-1 = 1/2 // : 1

x^-1 = 1/2

-1 < 0

1/(x^1) = 1/2 // * x^1

1 = 1/2*x^1 // : 1/2

2 = x^1

x = 2

x in { -13/4, 2 }

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