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D( x )
x-6 = 0
x^2-36 = 0
x+6 = 0
x-6 = 0
x-6 = 0
x-6 = 0 // + 6
x = 6
x^2-36 = 0
x^2-36 = 0
1*x^2 = 36 // : 1
x^2 = 36
x^2 = 36 // ^ 1/2
abs(x) = 6
x = 6 or x = -6
x+6 = 0
x+6 = 0
x+6 = 0 // - 6
x = -6
x in (-oo:-6) U (-6:6) U (6:+oo)
5/(x+6)-(1/(x-6)) = (2*x)/(x^2-36) // - (2*x)/(x^2-36)
5/(x+6)-(1/(x-6))-((2*x)/(x^2-36)) = 0
5/(x+6)-(x-6)^-1-2*x*(x^2-36)^-1 = 0
5/(x+6)-1/(x-6)+(-2*x)/(x^2-36) = 0
(5*(x-6)*(x^2-36))/((x+6)*(x-6)*(x^2-36))+(-1*(x+6)*(x^2-36))/((x+6)*(x-6)*(x^2-36))+(-2*x*(x+6)*(x-6))/((x+6)*(x-6)*(x^2-36)) = 0
5*(x-6)*(x^2-36)-1*(x+6)*(x^2-36)-2*x*(x+6)*(x-6) = 0
4*x^3-2*x^3-36*x^2-144*x+72*x+1296 = 0
2*x^3-36*x^2-72*x+1296 = 0
2*x^3-36*x^2-72*x+1296 = 0
2*(x^3-18*x^2-36*x+648) = 0
x^3-18*x^2-36*x+648 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 12, -12, 18, -18, 24, -24, 27, -27, 36, -36, 54, -54, 72, -72, 81, -81, 108, -108, 162, -162, 216, -216, 324, -324, 648, -648 }
1
x = 1
x^3-18*x^2-36*x+648 = 595
1
-1
x = -1
x^3-18*x^2-36*x+648 = 665
-1
2
x = 2
x^3-18*x^2-36*x+648 = 512
2
-2
x = -2
x^3-18*x^2-36*x+648 = 640
-2
3
x = 3
x^3-18*x^2-36*x+648 = 405
3
-3
x = -3
x^3-18*x^2-36*x+648 = 567
-3
4
x = 4
x^3-18*x^2-36*x+648 = 280
4
-4
x = -4
x^3-18*x^2-36*x+648 = 440
-4
6
x = 6
x^3-18*x^2-36*x+648 = 0
6
x-6
x^2-12*x-108
x^3-18*x^2-36*x+648
x-6
6*x^2-x^3
648-12*x^2-36*x
12*x^2-72*x
648-108*x
108*x-648
0
x^2-12*x-108 = 0
DELTA = (-12)^2-(-108*1*4)
DELTA = 576
DELTA > 0
x = (576^(1/2)+12)/(1*2) or x = (12-576^(1/2))/(1*2)
x = 18 or x = -6
x in { -6, 18, 6}
2*(x+6)*(x-18)*(x-6) = 0
(2*(x+6)*(x-18)*(x-6))/((x+6)*(x-6)*(x^2-36)) = 0
(2*(x+6)*(x-18)*(x-6))/((x+6)*(x-6)*(x^2-36)) = 0 // * (x+6)*(x-6)*(x^2-36)
2*(x+6)*(x-18)*(x-6) = 0
( x+6 )
x+6 = 0 // - 6
x = -6
( x-18 )
x-18 = 0 // + 18
x = 18
( x-6 )
x-6 = 0 // + 6
x = 6
x in { -6}
x in { 6}
x = 18
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