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D( x )
x+4 = 0
x^2-(2*x)-24 = 0
x+4 = 0
x+4 = 0
x+4 = 0 // - 4
x = -4
x^2-(2*x)-24 = 0
x^2-(2*x)-24 = 0
x^2-2*x-24 = 0
x^2-2*x-24 = 0
DELTA = (-2)^2-(-24*1*4)
DELTA = 100
DELTA > 0
x = (100^(1/2)+2)/(1*2) or x = (2-100^(1/2))/(1*2)
x = 6 or x = -4
x in (-oo:-4) U (-4:6) U (6:+oo)
8/(x+4) = (5*x)/(x^2-(2*x)-24)+1 // - (5*x)/(x^2-(2*x)-24)+1
8/(x+4)-((5*x)/(x^2-(2*x)-24))-1 = 0
8/(x+4)-5*x*(x^2-2*x-24)^-1-1 = 0
8/(x+4)+(-5*x)/(x^2-2*x-24)-1 = 0
x^2-2*x-24 = 0
x^2-2*x-24 = 0
x^2-2*x-24 = 0
DELTA = (-2)^2-(-24*1*4)
DELTA = 100
DELTA > 0
x = (100^(1/2)+2)/(1*2) or x = (2-100^(1/2))/(1*2)
x = 6 or x = -4
(x+4)*(x-6) = 0
8/(x+4)+(-5*x)/((x+4)*(x-6))-1 = 0
8/(x+4)+(-5*x)/(x+4)+(-1*(x+4))/(x+4) = 0
8-1*(x+4)-5*x = 0
8-5*x-x-4 = 0
4-6*x = 0
(4-6*x)/(x+4) = 0
(4-6*x)/(x+4) = 0 // * x+4
4-6*x = 0
4-6*x = 0 // - 4
-6*x = -4 // : -6
x = -4/(-6)
x = 2/3
x = 2/3
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