Question

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

Answer 1

$\frac{8}{t} + 5 = t - \frac{3}{t} + 5 + \frac{1}{3} \\ \\ 1. \: \frac{8}{t} = - \frac{3}{t} + \frac{1}{3} \\ \\ 2. \: 24 = 3t^{2} - 9 + t \\ \\ 3. \: 24 - 3t^{2} + 9 - t = 0 \\ \\ 4. \: 33 - 3t ^{2}- t = 0 \\ \\ 5. \: t = \frac{1 + \sqrt{397} }{ - 6} \: \frac{1 - \sqrt{397} }{ - 6} \\ \\ 6. \: t = - \frac{1 + \sqrt{397} }{6} \: - \frac{1 - \sqrt{397} }{6}$

Answer 2

Answer:

Final answer is t=7.

Step-by-step explanation:

$\frac{8}{t+5}=\frac{t-3}{t+5}+\frac{1}{3}$

$=\frac{8}{t+5}\cdot3\left(t+5\right)=\frac{t-3}{t+5}\cdot3\left(t+5\right)+\frac{1}{3}\cdot3\left(t+5\right)$

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

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

$24=4t-9+5$

$24=4t-4$

$24+4=4t$

$28=4t$

$\frac{28}{4}=t$

$7=t$

$t=7$

Hence final answer is t=7.