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D( x )
x^2-16 = 0
x+4 = 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-4 = 0
x-4 = 0
x-4 = 0 // + 4
x = 4
x in (-oo:-4) U (-4:4) U (4:+oo)
5/(x+4)-(4/(x-4)) = 3/(x^2-16) // - 3/(x^2-16)
5/(x+4)-(4/(x-4))-(3/(x^2-16)) = 0
5/(x+4)-4*(x-4)^-1-3*(x^2-16)^-1 = 0
5/(x+4)-4/(x-4)-3/(x^2-16) = 0
(5*(x-4)*(x^2-16))/((x+4)*(x-4)*(x^2-16))+(-4*(x+4)*(x^2-16))/((x+4)*(x-4)*(x^2-16))+(-3*(x+4)*(x-4))/((x+4)*(x-4)*(x^2-16)) = 0
5*(x-4)*(x^2-16)-4*(x+4)*(x^2-16)-3*(x+4)*(x-4) = 0
x^3-36*x^2-3*x^2-16*x+48+576 = 0
x^3-39*x^2-16*x+624 = 0
x^3-39*x^2-16*x+624 = 0
x^3-39*x^2-16*x+624 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 13, -13, 16, -16, 24, -24, 26, -26, 39, -39, 48, -48, 52, -52, 78, -78, 104, -104, 156, -156, 208, -208, 312, -312, 624, -624 }
1
x = 1
x^3-39*x^2-16*x+624 = 570
1
-1
x = -1
x^3-39*x^2-16*x+624 = 600
-1
2
x = 2
x^3-39*x^2-16*x+624 = 444
2
-2
x = -2
x^3-39*x^2-16*x+624 = 492
-2
3
x = 3
x^3-39*x^2-16*x+624 = 252
3
-3
x = -3
x^3-39*x^2-16*x+624 = 294
-3
4
x = 4
x^3-39*x^2-16*x+624 = 0
4
x-4
x^2-35*x-156
x^3-39*x^2-16*x+624
x-4
4*x^2-x^3
624-35*x^2-16*x
35*x^2-140*x
624-156*x
156*x-624
0
x^2-35*x-156 = 0
DELTA = (-35)^2-(-156*1*4)
DELTA = 1849
DELTA > 0
x = (1849^(1/2)+35)/(1*2) or x = (35-1849^(1/2))/(1*2)
x = 39 or x = -4
x in { -4, 39, 4}
(x+4)*(x-39)*(x-4) = 0
((x+4)*(x-39)*(x-4))/((x+4)*(x-4)*(x^2-16)) = 0
((x+4)*(x-39)*(x-4))/((x+4)*(x-4)*(x^2-16)) = 0 // * (x+4)*(x-4)*(x^2-16)
(x+4)*(x-39)*(x-4) = 0
( x+4 )
x+4 = 0 // - 4
x = -4
( x-39 )
x-39 = 0 // + 39
x = 39
( x-4 )
x-4 = 0 // + 4
x = 4
x in { -4}
x in { 4}
x = 39
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