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D( x )
x+2 = 0
x-2 = 0
x^2-4 = 0
x+2 = 0
x+2 = 0
x+2 = 0 // - 2
x = -2
x-2 = 0
x-2 = 0
x-2 = 0 // + 2
x = 2
x^2-4 = 0
x^2-4 = 0
1*x^2 = 4 // : 1
x^2 = 4
x^2 = 4 // ^ 1/2
abs(x) = 2
x = 2 or x = -2
x in (-oo:-2) U (-2:2) U (2:+oo)
20/(x^2-4)-(5/(x-2)) = 4/(x+2) // - 4/(x+2)
20/(x^2-4)-(5/(x-2))-(4/(x+2)) = 0
20/(x^2-4)-5*(x-2)^-1-4*(x+2)^-1 = 0
20/(x^2-4)-5/(x-2)-4/(x+2) = 0
(20*(x-2)*(x+2))/((x^2-4)*(x-2)*(x+2))+(-5*(x^2-4)*(x+2))/((x^2-4)*(x-2)*(x+2))+(-4*(x^2-4)*(x-2))/((x^2-4)*(x-2)*(x+2)) = 0
20*(x-2)*(x+2)-5*(x^2-4)*(x+2)-4*(x^2-4)*(x-2) = 0
10*x^2-5*x^3-4*x^3+8*x^2+20*x+16*x-40-32 = 0
18*x^2-9*x^3+36*x-72 = 0
18*x^2-9*x^3+36*x-72 = 0
9*(2*x^2-x^3+4*x-8) = 0
2*x^2-x^3+4*x-8 = 0
{ 1, -1, 2, -2, 4, -4, 8, -8 }
1
x = 1
2*x^2-x^3+4*x-8 = -3
1
-1
x = -1
2*x^2-x^3+4*x-8 = -9
-1
2
x = 2
2*x^2-x^3+4*x-8 = 0
2
x-2
4-x^2
2*x^2-x^3+4*x-8
x-2
x^3-2*x^2
4*x-8
8-4*x
0
4-x^2 = 0
DELTA = 0^2-(-1*4*4)
DELTA = 16
DELTA > 0
x = (16^(1/2)+0)/(-1*2) or x = (0-16^(1/2))/(-1*2)
x = -2 or x = 2
x in { -2, 2, 2}
9*(x+2)*(x-2)^2 = 0
(9*(x+2)*(x-2)^2)/((x^2-4)*(x-2)*(x+2)) = 0
(9*(x+2)*(x-2)^2)/((x^2-4)*(x-2)*(x+2)) = 0 // * (x^2-4)*(x-2)*(x+2)
9*(x+2)*(x-2)^2 = 0
( x+2 )
x+2 = 0 // - 2
x = -2
( x-2 )
x-2 = 0 // + 2
x = 2
x in { -2}
x in { 2}
x belongs to the empty set
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