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D( x )
x-3 = 0
x+3 = 0
x^2-9 = 0
x-3 = 0
x-3 = 0
x-3 = 0 // + 3
x = 3
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 (-3:3) U (3:+oo)
30/(x^2-9)-(5/(x-3)) = 8/(x+3) // - 8/(x+3)
30/(x^2-9)-(5/(x-3))-(8/(x+3)) = 0
30/(x^2-9)-5*(x-3)^-1-8*(x+3)^-1 = 0
30/(x^2-9)-5/(x-3)-8/(x+3) = 0
(30*(x-3)*(x+3))/((x^2-9)*(x-3)*(x+3))+(-5*(x^2-9)*(x+3))/((x^2-9)*(x-3)*(x+3))+(-8*(x^2-9)*(x-3))/((x^2-9)*(x-3)*(x+3)) = 0
30*(x-3)*(x+3)-5*(x^2-9)*(x+3)-8*(x^2-9)*(x-3) = 0
15*x^2-5*x^3-8*x^3+24*x^2+45*x+72*x-216-135 = 0
39*x^2-13*x^3+117*x-351 = 0
39*x^2-13*x^3+117*x-351 = 0
13*(3*x^2-x^3+9*x-27) = 0
3*x^2-x^3+9*x-27 = 0
{ 1, -1, 3, -3, 9, -9, 27, -27 }
1
x = 1
3*x^2-x^3+9*x-27 = -16
1
-1
x = -1
3*x^2-x^3+9*x-27 = -32
-1
3
x = 3
3*x^2-x^3+9*x-27 = 0
3
x-3
9-x^2
3*x^2-x^3+9*x-27
x-3
x^3-3*x^2
9*x-27
27-9*x
0
9-x^2 = 0
DELTA = 0^2-(-1*4*9)
DELTA = 36
DELTA > 0
x = (36^(1/2)+0)/(-1*2) or x = (0-36^(1/2))/(-1*2)
x = -3 or x = 3
x in { -3, 3, 3}
13*(x+3)*(x-3)^2 = 0
(13*(x+3)*(x-3)^2)/((x^2-9)*(x-3)*(x+3)) = 0
(13*(x+3)*(x-3)^2)/((x^2-9)*(x-3)*(x+3)) = 0 // * (x^2-9)*(x-3)*(x+3)
13*(x+3)*(x-3)^2 = 0
( x+3 )
x+3 = 0 // - 3
x = -3
( x-3 )
x-3 = 0 // + 3
x = 3
x in { -3}
x in { 3}
x belongs to the empty set
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