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D( t )
t-3 = 0
t+3 = 0
t^2-9 = 0
t-3 = 0
t-3 = 0
t-3 = 0 // + 3
t = 3
t+3 = 0
t+3 = 0
t+3 = 0 // - 3
t = -3
t^2-9 = 0
t^2-9 = 0
1*t^2 = 9 // : 1
t^2 = 9
t^2 = 9 // ^ 1/2
abs(t) = 3
t = 3 or t = -3
t in (-oo:-3) U (-3:3) U (3:+oo)
t/(t-3)+2/(t+3) = 18/(t^2-9) // - 18/(t^2-9)
t/(t-3)+2/(t+3)-(18/(t^2-9)) = 0
t/(t-3)+2/(t+3)-18*(t^2-9)^-1 = 0
t/(t-3)+2/(t+3)-18/(t^2-9) = 0
(t*(t+3)*(t^2-9))/((t-3)*(t+3)*(t^2-9))+(2*(t-3)*(t^2-9))/((t-3)*(t+3)*(t^2-9))+(-18*(t-3)*(t+3))/((t-3)*(t+3)*(t^2-9)) = 0
t*(t+3)*(t^2-9)+2*(t-3)*(t^2-9)-18*(t-3)*(t+3) = 0
t^4+5*t^3-15*t^2-18*t^2-45*t+54+162 = 0
t^4+5*t^3-33*t^2-45*t+216 = 0
t^4+5*t^3-33*t^2-45*t+216 = 0
t^4+5*t^3-33*t^2-45*t+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
t = 1
t^4+5*t^3-33*t^2-45*t+216 = 144
1
-1
t = -1
t^4+5*t^3-33*t^2-45*t+216 = 224
-1
2
t = 2
t^4+5*t^3-33*t^2-45*t+216 = 50
2
-2
t = -2
t^4+5*t^3-33*t^2-45*t+216 = 150
-2
3
t = 3
t^4+5*t^3-33*t^2-45*t+216 = 0
3
t-3
t^3+8*t^2-9*t-72
t^4+5*t^3-33*t^2-45*t+216
t-3
3*t^3-t^4
8*t^3-33*t^2-45*t+216
24*t^2-8*t^3
216-9*t^2-45*t
9*t^2-27*t
216-72*t
72*t-216
0
t^3+8*t^2-9*t-72 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 12, -12, 18, -18, 24, -24, 36, -36, 72, -72 }
1
t = 1
t^3+8*t^2-9*t-72 = -72
1
-1
t = -1
t^3+8*t^2-9*t-72 = -56
-1
2
t = 2
t^3+8*t^2-9*t-72 = -50
2
-2
t = -2
t^3+8*t^2-9*t-72 = -30
-2
3
t = 3
t^3+8*t^2-9*t-72 = 0
3
t-3
t^2+11*t+24
t^3+8*t^2-9*t-72
t-3
3*t^2-t^3
11*t^2-9*t-72
33*t-11*t^2
24*t-72
72-24*t
0
t^2+11*t+24 = 0
DELTA = 11^2-(1*4*24)
DELTA = 25
DELTA > 0
t = (25^(1/2)-11)/(1*2) or t = (-25^(1/2)-11)/(1*2)
t = -3 or t = -8
t in { -8, -3, 3, 3}
(t+8)*(t+3)*(t-3)^2 = 0
((t+8)*(t+3)*(t-3)^2)/((t-3)*(t+3)*(t^2-9)) = 0
((t+8)*(t+3)*(t-3)^2)/((t-3)*(t+3)*(t^2-9)) = 0 // * (t-3)*(t+3)*(t^2-9)
(t+8)*(t+3)*(t-3)^2 = 0
( t+3 )
t+3 = 0 // - 3
t = -3
( t+8 )
t+8 = 0 // - 8
t = -8
( t-3 )
t-3 = 0 // + 3
t = 3
t in { -3}
t in { 3}
t = -8
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