Question

Solve 8/t+5 = t-3/t+5 + 1/3

Answer 1

`(8)/(t) + 5 = t - (3)/(t) + 5 + (1)/(3) \\ \\ 1. \: (8)/(t) = - (3)/(t) + (1)/(3) \\ \\ 2. \: 24 = 3t^(2) - 9 + t \\ \\ 3. \: 24 - 3t^(2) + 9 - t = 0 \\ \\ 4. \: 33 - 3t ^(2)- t = 0 \\ \\ 5. \: t = (1 + √(397) )/( - 6) \: (1 - √(397) )/( - 6) \\ \\ 6. \: t = - (1 + √(397) )/(6) \: - (1 - √(397) )/(6)`

Answer 2

Final answer is t=7.

Explanation:

`(8)/(t+5)=(t-3)/(t+5)+(1)/(3)`

`=(8)/(t+5)\cdot3\left(t+5\right)=(t-3)/(t+5)\cdot3\left(t+5\right)+(1)/(3)\cdot3\left(t+5\right)`

`8\cdot3=3\left(t-3\right)+\left(t+5\right)`

`24=3t-9+t+5`

`24=4t-9+5`

`24=4t-4`

`24+4=4t`

`28=4t`

`(28)/(4)=t`

`7=t`

`t=7`

Hence final answer is t=7.