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D( x )
x+5 = 0
x = 0
x+5 = 0
x+5 = 0
x+5 = 0 // - 5
x = -5
x = 0
x = 0
x in (-oo:-5) U (-5:0) U (0:+oo)
8/(x+5)+6/x = 3 // - 3
8/(x+5)+6/x-3 = 0
(8*x)/(x*(x+5))+(6*(x+5))/(x*(x+5))+(-3*x*(x+5))/(x*(x+5)) = 0
6*(x+5)-3*x*(x+5)+8*x = 0
14*x-3*x^2-15*x+30 = 0
30-3*x^2-x = 0
30-3*x^2-x = 0
30-3*x^2-x = 0
DELTA = (-1)^2-(-3*4*30)
DELTA = 361
DELTA > 0
x = (361^(1/2)+1)/(-3*2) or x = (1-361^(1/2))/(-3*2)
x = -10/3 or x = 3
(x+10/3)*(x-3) = 0
((x+10/3)*(x-3))/(x*(x+5)) = 0
((x+10/3)*(x-3))/(x*(x+5)) = 0 // * x*(x+5)
(x+10/3)*(x-3) = 0
( x+10/3 )
x+10/3 = 0 // - 10/3
x = -10/3
( x-3 )
x-3 = 0 // + 3
x = 3
x in { -10/3, 3 }
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