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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(3*x-4)/5+13/x = 8/x+4 // - 8/x+4
(3*x-4)/5+13/x-(8/x)-4 = 0
(3*x-4)/5+13/x-8*x^-1-4 = 0
(3*x-4)/5+13/x-8/x-4 = 0
(x*(3*x-4))/(5*x)+(5*13)/(5*x)+(-8*5)/(5*x)+(-4*5*x)/(5*x) = 0
x*(3*x-4)-4*5*x+5*13-8*5 = 0
3*x^2-4*x-20*x-40+65 = 0
3*x^2-4*x-20*x+25 = 0
3*x^2-24*x+25 = 0
3*x^2-24*x+25 = 0
3*x^2-24*x+25 = 0
DELTA = (-24)^2-(3*4*25)
DELTA = 276
DELTA > 0
x = (276^(1/2)+24)/(2*3) or x = (24-276^(1/2))/(2*3)
x = (2*69^(1/2)+24)/6 or x = (24-2*69^(1/2))/6
(x-((24-2*69^(1/2))/6))*(x-((2*69^(1/2)+24)/6)) = 0
((x-((24-2*69^(1/2))/6))*(x-((2*69^(1/2)+24)/6)))/(5*x) = 0
((x-((24-2*69^(1/2))/6))*(x-((2*69^(1/2)+24)/6)))/(5*x) = 0 // * 5*x
(x-((24-2*69^(1/2))/6))*(x-((2*69^(1/2)+24)/6)) = 0
( x-((2*69^(1/2)+24)/6) )
x-((2*69^(1/2)+24)/6) = 0 // + (2*69^(1/2)+24)/6
x = (2*69^(1/2)+24)/6
( x-((24-2*69^(1/2))/6) )
x-((24-2*69^(1/2))/6) = 0 // + (24-2*69^(1/2))/6
x = (24-2*69^(1/2))/6
x in { (2*69^(1/2)+24)/6, (24-2*69^(1/2))/6 }
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