Find the natural number n for which (n!)/((n - 2)!) = 132. Then find x if 1/(6!) + 1/(7!) = x/(8!).

Step 1. The ratio. $\dfrac{n!}{(n - 2)!} = n(n - 1) = 132$.

Step 2. Two numbers in a row. $12 \times 11 = 132$, so $n = 12$. (The other root, $-11$, is not a natural number.)

Step 3. Clear the fractions. $\dfrac{8!}{6!} + \dfrac{8!}{7!} = x$, so $x = 8 \times 7 + 8 = 64$.