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D( x )
x = 0
x+3 = 0
x^2-9 = 0
x = 0
x = 0
x+3 = 0
x+3 = 0
x+3 = 0 // - 3
x = -3
x^2-9 = 0
x^2-9 = 0
1*x^2 = 9 // : 1
x^2 = 9
x^2 = 9 // ^ 1/2
abs(x) = 3
x = 3 or x = -3
x in (-oo:-3) U (-3:0) U (0:3) U (3:+oo)
(6*x+6)/(x^2-9)-(2/(x+3)) = 3/x-3 // - 3/x-3
(6*x+6)/(x^2-9)-(2/(x+3))-(3/x)+3 = 0
(6*x+6)/(x^2-9)-2*(x+3)^-1-3*x^-1+3 = 0
(6*x+6)/(x^2-9)-2/(x+3)-3/x+3 = 0
(x*(6*x+6)*(x+3))/(x*(x^2-9)*(x+3))+(-2*x*(x^2-9))/(x*(x^2-9)*(x+3))+(-3*(x^2-9)*(x+3))/(x*(x^2-9)*(x+3))+(3*x*(x^2-9)*(x+3))/(x*(x^2-9)*(x+3)) = 0
x*(6*x+6)*(x+3)-2*x*(x^2-9)-3*(x^2-9)*(x+3)+3*x*(x^2-9)*(x+3) = 0
3*x^4+4*x^3-3*x^3+9*x^3+24*x^2-9*x^2-27*x^2+36*x+27*x-81*x+81 = 0
3*x^4+x^3+9*x^3+15*x^2-27*x^2+63*x-81*x+81 = 0
3*x^4+10*x^3-12*x^2-18*x+81 = 0
3*x^4+10*x^3-12*x^2-18*x+81 = 0
3*x^4+10*x^3-12*x^2-18*x+81 = 0
{ 1, -1, 3, -3, 9, -9, 27, -27, 81, -81 }
1
x = 1
3*x^4+10*x^3-12*x^2-18*x+81 = 64
1
-1
x = -1
3*x^4+10*x^3-12*x^2-18*x+81 = 80
-1
3
x = 3
3*x^4+10*x^3-12*x^2-18*x+81 = 432
3
-3
x = -3
3*x^4+10*x^3-12*x^2-18*x+81 = 0
-3
x+3
3*x^3+x^2-15*x+27
3*x^4+10*x^3-12*x^2-18*x+81
x+3
-3*x^4-9*x^3
x^3-12*x^2-18*x+81
-x^3-3*x^2
81-15*x^2-18*x
15*x^2+45*x
27*x+81
-27*x-81
0
3*x^3+x^2-15*x+27 = 0
{ 1, -1, 3, -3, 9, -9, 27, -27 }
1
x = 1
3*x^3+x^2-15*x+27 = 16
1
-1
x = -1
3*x^3+x^2-15*x+27 = 40
-1
3
x = 3
3*x^3+x^2-15*x+27 = 72
3
-3
x = -3
3*x^3+x^2-15*x+27 = 0
-3
x+3
3*x^2-8*x+9
3*x^3+x^2-15*x+27
x+3
-3*x^3-9*x^2
27-8*x^2-15*x
8*x^2+24*x
9*x+27
-9*x-27
0
3*x^2-8*x+9 = 0
DELTA = (-8)^2-(3*4*9)
DELTA = -44
DELTA < 0
x in { -3, -3}
(x+3)^2 = 0
((x+3)^2)/(x*(x^2-9)*(x+3)) = 0
((x+3)^2)/(x*(x^2-9)*(x+3)) = 0 // * x*(x^2-9)*(x+3)
(x+3)^2 = 0
x+3 = 0 // - 3
x = -3
x in { -3}
x belongs to the empty set
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