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D( t )
t+7 = 0
t^2+10*t+21 = 0
t+3 = 0
t+7 = 0
t+7 = 0
t+7 = 0 // - 7
t = -7
t^2+10*t+21 = 0
t^2+10*t+21 = 0
t^2+10*t+21 = 0
DELTA = 10^2-(1*4*21)
DELTA = 16
DELTA > 0
t = (16^(1/2)-10)/(1*2) or t = (-16^(1/2)-10)/(1*2)
t = -3 or t = -7
t+3 = 0
t+3 = 0
t+3 = 0 // - 3
t = -3
t in (-oo:-7) U (-7:-3) U (-3:+oo)
1/(t+3)+3/(t+7) = 4/(t^2+10*t+21) // - 4/(t^2+10*t+21)
1/(t+3)+3/(t+7)-(4/(t^2+10*t+21)) = 0
1/(t+3)+3/(t+7)-4*(t^2+10*t+21)^-1 = 0
1/(t+3)+3/(t+7)-4/(t^2+10*t+21) = 0
t^2+10*t+21 = 0
t^2+10*t+21 = 0
t^2+10*t+21 = 0
DELTA = 10^2-(1*4*21)
DELTA = 16
DELTA > 0
t = (16^(1/2)-10)/(1*2) or t = (-16^(1/2)-10)/(1*2)
t = -3 or t = -7
(t+7)*(t+3) = 0
1/(t+3)+3/(t+7)-4/((t+7)*(t+3)) = 0
(1*(t+7))/((t+3)*(t+7))+(3*(t+3))/((t+3)*(t+7))-4/((t+3)*(t+7)) = 0
1*(t+7)+3*(t+3)-4 = 0
4*t-4+16 = 0
4*t+12 = 0
(4*t+12)/((t+3)*(t+7)) = 0
(4*t+12)/((t+3)*(t+7)) = 0 // * (t+3)*(t+7)
4*t+12 = 0
4*t+12 = 0 // - 12
4*t = -12 // : 4
t = -12/4
t = -3
t in { -3}
t belongs to the empty set
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