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D( x )
x+2 = 0
x = 0
x+2 = 0
x+2 = 0
x+2 = 0 // - 2
x = -2
x = 0
x = 0
x in (-oo:-2) U (-2:0) U (0:+oo)
(3/2)*x+2/x-2-2 = (8/(x+2))*(x-2) // - (8/(x+2))*(x-2)
(3/2)*x-((8/(x+2))*(x-2))+2/x-2-2 = 0
(3/2)*x-8*(x+2)^-1*(x-2)+2/x-2-2 = 0
(-8*(x-2))/(x+2)+(3*x)/2+2/x-2-2 = 0
(-8*2*x*(x-2))/(2*x*(x+2))+(3*x*x*(x+2))/(2*x*(x+2))+(2^2*(x+2))/(2*x*(x+2))+(-2*2*x*(x+2))/(2*x*(x+2))+(-2*2*x*(x+2))/(2*x*(x+2)) = 0
3*x*x*(x+2)-8*2*x*(x-2)+2^2*(x+2)-2*2*x*(x+2)-2*2*x*(x+2) = 0
3*x^3-10*x^2-4*x^2-4*x^2+32*x+4*x-8*x-8*x+8 = 0
3*x^3-10*x^2-4*x^2-4*x^2+36*x-8*x-8*x+8 = 0
3*x^3-14*x^2-4*x^2+28*x-8*x+8 = 0
3*x^3-18*x^2+20*x+8 = 0
3*x^3-18*x^2+20*x+8 = 0
3*x^3-18*x^2+20*x+8 = 0
{ 1, -1, 2, -2, 4, -4, 8, -8 }
1
x = 1
3*x^3-18*x^2+20*x+8 = 13
1
-1
x = -1
3*x^3-18*x^2+20*x+8 = -33
-1
2
x = 2
3*x^3-18*x^2+20*x+8 = 0
2
x-2
3*x^2-12*x-4
3*x^3-18*x^2+20*x+8
x-2
6*x^2-3*x^3
20*x-12*x^2+8
12*x^2-24*x
8-4*x
4*x-8
0
3*x^2-12*x-4 = 0
DELTA = (-12)^2-(-4*3*4)
DELTA = 192
DELTA > 0
x = (192^(1/2)+12)/(2*3) or x = (12-192^(1/2))/(2*3)
x = (8*3^(1/2)+12)/6 or x = (12-8*3^(1/2))/6
x in { (12-8*3^(1/2))/6, (8*3^(1/2)+12)/6, 2}
(x-((12-8*3^(1/2))/6))*(x-((8*3^(1/2)+12)/6))*(x-2) = 0
((x-((12-8*3^(1/2))/6))*(x-((8*3^(1/2)+12)/6))*(x-2))/(2*x*(x+2)) = 0
((x-((12-8*3^(1/2))/6))*(x-((8*3^(1/2)+12)/6))*(x-2))/(2*x*(x+2)) = 0 // * 2*x*(x+2)
(x-((12-8*3^(1/2))/6))*(x-((8*3^(1/2)+12)/6))*(x-2) = 0
( x-((12-8*3^(1/2))/6) )
x-((12-8*3^(1/2))/6) = 0 // + (12-8*3^(1/2))/6
x = (12-8*3^(1/2))/6
( x-((8*3^(1/2)+12)/6) )
x-((8*3^(1/2)+12)/6) = 0 // + (8*3^(1/2)+12)/6
x = (8*3^(1/2)+12)/6
( x-2 )
x-2 = 0 // + 2
x = 2
x in { (12-8*3^(1/2))/6, (8*3^(1/2)+12)/6, 2 }
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