3/(t+3)-1/t=5/(2t+6)

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Solution for 3/(t+3)-1/t=5/(2t+6) equation:


D( t )

t+3 = 0

2*t+6 = 0

t = 0

t+3 = 0

t+3 = 0

t+3 = 0 // - 3

t = -3

2*t+6 = 0

2*t+6 = 0

2*t+6 = 0 // - 6

2*t = -6 // : 2

t = -6/2

t = -3

t = 0

t = 0

t in (-oo:-3) U (-3:0) U (0:+oo)

3/(t+3)-(1/t) = 5/(2*t+6) // - 5/(2*t+6)

3/(t+3)-(5/(2*t+6))-(1/t) = 0

3/(t+3)-5*(2*t+6)^-1-t^-1 = 0

3/(t+3)-5/(2*t+6)-1/t = 0

(3*t*(2*t+6))/(t*(t+3)*(2*t+6))+(-5*t*(t+3))/(t*(t+3)*(2*t+6))+(-1*(t+3)*(2*t+6))/(t*(t+3)*(2*t+6)) = 0

3*t*(2*t+6)-5*t*(t+3)-1*(t+3)*(2*t+6) = 0

t^2-2*t^2+3*t-12*t-18 = 0

-t^2-9*t-18 = 0

-t^2-9*t-18 = 0

-1*(t^2+9*t+18) = 0

t^2+9*t+18 = 0

DELTA = 9^2-(1*4*18)

DELTA = 9

DELTA > 0

t = (9^(1/2)-9)/(1*2) or t = (-9^(1/2)-9)/(1*2)

t = -3 or t = -6

-1*(t+6)*(t+3) = 0

(-1*(t+6)*(t+3))/(t*(t+3)*(2*t+6)) = 0

(-1*(t+6)*(t+3))/(t*(t+3)*(2*t+6)) = 0 // * t*(t+3)*(2*t+6)

-1*(t+6)*(t+3) = 0

( t+3 )

t+3 = 0 // - 3

t = -3

( t+6 )

t+6 = 0 // - 6

t = -6

t in { -3}

t = -6

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