((3t)/(t-7)(t+7))+((t)/(t+7))

Solution for ((3t)/(t-7)(t+7))+((t)/(t+7)) equation:

D( t )

t+7 = 0

t-7 = 0

t+7 = 0

t+7 = 0

t+7 = 0 // - 7

t = -7

t-7 = 0

t-7 = 0

t-7 = 0 // + 7

t = 7

t in (-oo:-7) U (-7:7) U (7:+oo)

((3*t)/(t-7))*(t+7)+t/(t+7) = 0

(3*t*(t+7))/(t-7)+t/(t+7) = 0

(3*t*(t+7)^2)/((t-7)*(t+7))+(t*(t-7))/((t-7)*(t+7)) = 0

3*t*(t+7)^2+t*(t-7) = 0

3*t^3+43*t^2+140*t = 0

3*t^3+43*t^2+140*t = 0

t*(3*t^2+43*t+140) = 0

3*t^2+43*t+140 = 0

DELTA = 43^2-(3*4*140)

DELTA = 169

DELTA > 0

t = (169^(1/2)-43)/(2*3) or t = (-169^(1/2)-43)/(2*3)

t = -5 or t = -28/3

t*(t+28/3)*(t+5) = 0

(t*(t+28/3)*(t+5))/((t-7)*(t+7)) = 0

(t*(t+28/3)*(t+5))/((t-7)*(t+7)) = 0 // * (t-7)*(t+7)

t*(t+28/3)*(t+5) = 0

( t+28/3 )

t+28/3 = 0 // - 28/3

t = -28/3

( t+5 )

t+5 = 0 // - 5

t = -5

( t )

t = 0

t in { -28/3, -5, 0 }