https://file.aiquickdraw.com/mathbot/file/1729979585573p15y0md3.jpg

The equation shown in the image is:

\[
\frac{n! - (n-1)!}{(n+1)!} = \frac{1}{6}
\]

Let's analyze and solve this equation step-by-step.

1. **Rewrite the Factorials:** Start by expressing each factorial in terms of \(n\) and simplifying where possible.

2. **Simplify \( n! - (n-1)! \):**
   - Recall that \( n! = n \cdot (n-1)! \).
   - So, \( n! - (n-1)! = n \cdot (n-1)! - (n-1)! \).
   - Factor out \( (n-1)! \):
     \[
     n! - (n-1)! = (n - 1)! \cdot (n - 1)
     \]

3. **Substitute and Simplify the Left Side of the Equation:**


Solve the equation \( \frac{n! - (n-1)!}{(n+1)!} = \frac{1}{6} \).

Learn how to solve the factorial equation \( \frac{n! - (n-1)!}{(n+1)!} = \frac{1}{6} \) with a step-by-step solution. This problem involves simplification of factorials and algebraic techniques, suitable for students in Grades 10-12.

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