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D( x )
x^2-16 = 0
x-4 = 0
x^2-16 = 0
x^2-16 = 0
1*x^2 = 16 // : 1
x^2 = 16
x^2 = 16 // ^ 1/2
abs(x) = 4
x = 4 or x = -4
x-4 = 0
x-4 = 0
x-4 = 0 // + 4
x = 4
x in (-oo:-4) U (-4:4) U (4:+oo)
8/(x^2-16)-(1/(x-4)) = 1 // - 1
8/(x^2-16)-(1/(x-4))-1 = 0
8/(x^2-16)-(x-4)^-1-1 = 0
8/(x^2-16)-1/(x-4)-1 = 0
(8*(x-4))/((x^2-16)*(x-4))+(-1*(x^2-16))/((x^2-16)*(x-4))+(-1*(x^2-16)*(x-4))/((x^2-16)*(x-4)) = 0
8*(x-4)-1*(x^2-16)-1*(x^2-16)*(x-4) = 0
4*x^2-x^3-x^2+8*x+16*x-64-16 = 0
3*x^2-x^3+24*x-80 = 0
3*x^2-x^3+24*x-80 = 0
3*x^2-x^3+24*x-80 = 0
{ 1, -1, 2, -2, 4, -4, 5, -5, 8, -8, 10, -10, 16, -16, 20, -20, 40, -40, 80, -80 }
1
x = 1
3*x^2-x^3+24*x-80 = -54
1
-1
x = -1
3*x^2-x^3+24*x-80 = -100
-1
2
x = 2
3*x^2-x^3+24*x-80 = -28
2
-2
x = -2
3*x^2-x^3+24*x-80 = -108
-2
4
x = 4
3*x^2-x^3+24*x-80 = 0
4
x-4
20-x^2-x
3*x^2-x^3+24*x-80
x-4
x^3-4*x^2
24*x-x^2-80
x^2-4*x
20*x-80
80-20*x
0
20-x^2-x = 0
DELTA = (-1)^2-(-1*4*20)
DELTA = 81
DELTA > 0
x = (81^(1/2)+1)/(-1*2) or x = (1-81^(1/2))/(-1*2)
x = -5 or x = 4
x in { -5, 4, 4}
(x+5)*(x-4)^2 = 0
((x+5)*(x-4)^2)/((x^2-16)*(x-4)) = 0
((x+5)*(x-4)^2)/((x^2-16)*(x-4)) = 0 // * (x^2-16)*(x-4)
(x+5)*(x-4)^2 = 0
( x+5 )
x+5 = 0 // - 5
x = -5
( x-4 )
x-4 = 0 // + 4
x = 4
x in { 4}
x = -5
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