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D( x )
x+4 = 0
x^2-16 = 0
x-4 = 0
x+4 = 0
x+4 = 0
x+4 = 0 // - 4
x = -4
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)
40/(x^2-16)-(5/(x-4)) = 8/(x+4) // - 8/(x+4)
40/(x^2-16)-(5/(x-4))-(8/(x+4)) = 0
40/(x^2-16)-5*(x-4)^-1-8*(x+4)^-1 = 0
40/(x^2-16)-5/(x-4)-8/(x+4) = 0
(40*(x-4)*(x+4))/((x^2-16)*(x-4)*(x+4))+(-5*(x^2-16)*(x+4))/((x^2-16)*(x-4)*(x+4))+(-8*(x^2-16)*(x-4))/((x^2-16)*(x-4)*(x+4)) = 0
40*(x-4)*(x+4)-5*(x^2-16)*(x+4)-8*(x^2-16)*(x-4) = 0
20*x^2-5*x^3-8*x^3+32*x^2+80*x+128*x-512-320 = 0
52*x^2-13*x^3+208*x-832 = 0
52*x^2-13*x^3+208*x-832 = 0
13*(4*x^2-x^3+16*x-64) = 0
4*x^2-x^3+16*x-64 = 0
{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64 }
1
x = 1
4*x^2-x^3+16*x-64 = -45
1
-1
x = -1
4*x^2-x^3+16*x-64 = -75
-1
2
x = 2
4*x^2-x^3+16*x-64 = -24
2
-2
x = -2
4*x^2-x^3+16*x-64 = -72
-2
4
x = 4
4*x^2-x^3+16*x-64 = 0
4
x-4
16-x^2
4*x^2-x^3+16*x-64
x-4
x^3-4*x^2
16*x-64
64-16*x
0
16-x^2 = 0
DELTA = 0^2-(-1*4*16)
DELTA = 64
DELTA > 0
x = (64^(1/2)+0)/(-1*2) or x = (0-64^(1/2))/(-1*2)
x = -4 or x = 4
x in { -4, 4, 4}
13*(x+4)*(x-4)^2 = 0
(13*(x+4)*(x-4)^2)/((x^2-16)*(x-4)*(x+4)) = 0
(13*(x+4)*(x-4)^2)/((x^2-16)*(x-4)*(x+4)) = 0 // * (x^2-16)*(x-4)*(x+4)
13*(x+4)*(x-4)^2 = 0
( x+4 )
x+4 = 0 // - 4
x = -4
( x-4 )
x-4 = 0 // + 4
x = 4
x in { -4}
x in { 4}
x belongs to the empty set
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