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D( x )
x = 0
x+6 = 0
2*x+12 = 0
x = 0
x = 0
x+6 = 0
x+6 = 0
x+6 = 0 // - 6
x = -6
2*x+12 = 0
2*x+12 = 0
2*x+12 = 0 // - 12
2*x = -12 // : 2
x = -12/2
x = -6
x in (-oo:-6) U (-6:0) U (0:+oo)
6/(2*x+12)+6/(x+6)+6/x = 1 // - 1
6/(2*x+12)+6/(x+6)+6/x-1 = 0
(6*x*(x+6))/(x*(2*x+12)*(x+6))+(6*x*(2*x+12))/(x*(2*x+12)*(x+6))+(6*(2*x+12)*(x+6))/(x*(2*x+12)*(x+6))+(-1*x*(2*x+12)*(x+6))/(x*(2*x+12)*(x+6)) = 0
6*x*(x+6)+6*x*(2*x+12)+6*(2*x+12)*(x+6)-1*x*(2*x+12)*(x+6) = 0
18*x^2-2*x^3+12*x^2-24*x^2+108*x+144*x-72*x+432 = 0
30*x^2-2*x^3-24*x^2+252*x-72*x+432 = 0
6*x^2-2*x^3+180*x+432 = 0
6*x^2-2*x^3+180*x+432 = 0
2*(3*x^2-x^3+90*x+216) = 0
3*x^2-x^3+90*x+216 = 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, 108, -108, 216, -216 }
1
x = 1
3*x^2-x^3+90*x+216 = 308
1
-1
x = -1
3*x^2-x^3+90*x+216 = 130
-1
2
x = 2
3*x^2-x^3+90*x+216 = 400
2
-2
x = -2
3*x^2-x^3+90*x+216 = 56
-2
3
x = 3
3*x^2-x^3+90*x+216 = 486
3
-3
x = -3
3*x^2-x^3+90*x+216 = 0
-3
x+3
6*x-x^2+72
3*x^2-x^3+90*x+216
x+3
x^3+3*x^2
6*x^2+90*x+216
-6*x^2-18*x
72*x+216
-72*x-216
0
6*x-x^2+72 = 0
DELTA = 6^2-(-1*4*72)
DELTA = 324
DELTA > 0
x = (324^(1/2)-6)/(-1*2) or x = (-324^(1/2)-6)/(-1*2)
x = -6 or x = 12
x in { -6, 12, -3}
2*(x+6)*(x-12)*(x+3) = 0
(2*(x+6)*(x-12)*(x+3))/(x*(2*x+12)*(x+6)) = 0
(2*(x+6)*(x-12)*(x+3))/(x*(2*x+12)*(x+6)) = 0 // * x*(2*x+12)*(x+6)
2*(x+6)*(x-12)*(x+3) = 0
( x+3 )
x+3 = 0 // - 3
x = -3
( x+6 )
x+6 = 0 // - 6
x = -6
( x-12 )
x-12 = 0 // + 12
x = 12
x in { -6}
x in { -3, 12 }
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