(1/x+5)-(8/x-5)=(4/x^2-25)

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Solution for (1/x+5)-(8/x-5)=(4/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)

1/x-(8/x)+5+5 = 4/(x^2)-25 // - 4/(x^2)-25

1/x-(8/x)-(4/(x^2))+5+5+25 = 0

1/x-8*x^-1-4*x^-2+5+5+25 = 0

35-7*x^-1-4*x^-2 = 0

t_1 = x^-1

35-4*t_1^2-7*t_1^1 = 0

35-4*t_1^2-7*t_1 = 0

DELTA = (-7)^2-(-4*4*35)

DELTA = 609

DELTA > 0

t_1 = (609^(1/2)+7)/(-4*2) or t_1 = (7-609^(1/2))/(-4*2)

t_1 = (609^(1/2)+7)/(-8) or t_1 = (7-609^(1/2))/(-8)

t_1 = (609^(1/2)+7)/(-8)

x^-1-((609^(1/2)+7)/(-8)) = 0

1*x^-1 = (609^(1/2)+7)/(-8) // : 1

x^-1 = (609^(1/2)+7)/(-8)

-1 < 0

1/(x^1) = (609^(1/2)+7)/(-8) // * x^1

1 = ((609^(1/2)+7)/(-8))*x^1 // : (609^(1/2)+7)/(-8)

-8*(609^(1/2)+7)^-1 = x^1

x = -8*(609^(1/2)+7)^-1

t_1 = (7-609^(1/2))/(-8)

x^-1-((7-609^(1/2))/(-8)) = 0

1*x^-1 = (7-609^(1/2))/(-8) // : 1

x^-1 = (7-609^(1/2))/(-8)

-1 < 0

1/(x^1) = (7-609^(1/2))/(-8) // * x^1

1 = ((7-609^(1/2))/(-8))*x^1 // : (7-609^(1/2))/(-8)

-8*(7-609^(1/2))^-1 = x^1

x = -8*(7-609^(1/2))^-1

x in { -8*(609^(1/2)+7)^-1, -8*(7-609^(1/2))^-1 }

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