Answer :

We are given the equation:
[tex]$$
\frac{5}{6} + \frac{1}{\square} = \frac{14}{15}.
$$[/tex]

Step 1. Isolate the unknown fraction by subtracting [tex]$\frac{5}{6}$[/tex] from both sides:
[tex]$$
\frac{1}{\square} = \frac{14}{15} - \frac{5}{6}.
$$[/tex]

Step 2. To subtract the fractions, find a common denominator. The denominators are [tex]$15$[/tex] and [tex]$6$[/tex], and their least common denominator is [tex]$30$[/tex]. Rewrite each fraction with a denominator of [tex]$30$[/tex]:
[tex]$$
\frac{14}{15} = \frac{14 \times 2}{15 \times 2} = \frac{28}{30}, \quad \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}.
$$[/tex]

Step 3. Subtract the fractions:
[tex]$$
\frac{1}{\square} = \frac{28}{30} - \frac{25}{30} = \frac{3}{30}.
$$[/tex]
Simplify [tex]$\frac{3}{30}$[/tex] by dividing the numerator and denominator by [tex]$3$[/tex]:
[tex]$$
\frac{3}{30} = \frac{1}{10}.
$$[/tex]

Step 4. Now we have:
[tex]$$
\frac{1}{\square} = \frac{1}{10}.
$$[/tex]
Since both fractions have numerator [tex]$1$[/tex], the denominators must be equal. Therefore:
[tex]$$
\square = 10.
$$[/tex]

The missing number is [tex]$\boxed{10}$[/tex].

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