What fraction completes the rule for the arithmetic sequence shown below? Give your answer in its simplest form.
Rule:
Start at $\frac{6}{t+1}$
Add each time
\[
\frac{6}{t+1} \rightarrow \frac{4 t+34}{5(t+1)} \rightarrow \frac{8 t+38}{5(t+1)}
\]

Step 1 ：Find the common difference between the terms in the arithmetic sequence by subtracting the first term from the second term and then subtracting the second term from the third term.

Step 2 ：\(t = t\)

Step 3 ：\(term1 = \frac{6}{t + 1}\)

Step 4 ：\(term2 = \frac{4t + 34}{5(t + 1)}\)

Step 5 ：\(term3 = \frac{8t + 38}{5(t + 1)}\)

Step 6 ：\(difference1 = term2 - term1 = \frac{4}{5}\)

Step 7 ：\(difference2 = term3 - term2 = \frac{4}{5}\)

Step 8 ：Since the differences are equal, we have found the common difference.

Step 9 ：\(\boxed{\frac{4}{5}}\) is the fraction that completes the rule for the arithmetic sequence.