To simplify the given expression, we can start by breaking it down into its individual fractions:

(3/n! + 5/(n+1)!) / (7/n! - 6n/(n+1)!)

Next, we can find common denominators for each fraction within the larger expression:

(3(n+1) + 5n) / (7(n+1) - 6n)

This simplifies to:

(3n + 3 + 5n) / (7n + 7 - 6n)

Combining like terms:

(8n + 3) / (n + 7)

Therefore, the simplified expression is (8n + 3) / (n + 7).