2/x-5-1/x-5=11/x^2-25

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Solution for 2/x-5-1/x-5=11/x^2-25 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)

2/x-(1/x)-5-5 = 11/(x^2)-25 // - 11/(x^2)-25

2/x-(1/x)-(11/(x^2))-5-5+25 = 0

2/x-x^-1-11*x^-2-5-5+25 = 0

x^-1-11*x^-2+15 = 0

t_1 = x^-1

1*t_1^1-11*t_1^2+15 = 0

t_1-11*t_1^2+15 = 0

DELTA = 1^2-(-11*4*15)

DELTA = 661

DELTA > 0

t_1 = (661^(1/2)-1)/(-11*2) or t_1 = (-661^(1/2)-1)/(-11*2)

t_1 = (661^(1/2)-1)/(-22) or t_1 = (661^(1/2)+1)/22

t_1 = (661^(1/2)-1)/(-22)

x^-1-((661^(1/2)-1)/(-22)) = 0

1*x^-1 = (661^(1/2)-1)/(-22) // : 1

x^-1 = (661^(1/2)-1)/(-22)

-1 < 0

1/(x^1) = (661^(1/2)-1)/(-22) // * x^1

1 = ((661^(1/2)-1)/(-22))*x^1 // : (661^(1/2)-1)/(-22)

-22*(661^(1/2)-1)^-1 = x^1

x = -22*(661^(1/2)-1)^-1

t_1 = (661^(1/2)+1)/22

x^-1-((661^(1/2)+1)/22) = 0

1*x^-1 = (661^(1/2)+1)/22 // : 1

x^-1 = (661^(1/2)+1)/22

-1 < 0

1/(x^1) = (661^(1/2)+1)/22 // * x^1

1 = ((661^(1/2)+1)/22)*x^1 // : (661^(1/2)+1)/22

22*(661^(1/2)+1)^-1 = x^1

x = 22*(661^(1/2)+1)^-1

x in { -22*(661^(1/2)-1)^-1, 22*(661^(1/2)+1)^-1 }

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