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).
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).