To solve the expression $3 - \left(\frac{4}{5} - \frac{5}{6}\right)$, follow these steps:

1. First, find the common denominator for the fractions $\frac{4}{5}$ and $\frac{5}{6}$. The least common denominator (LCD) of 5 and 6 is 30.

   • Convert $\frac{4}{5}$ to $\frac{24}{30}$ by multiplying both the numerator and denominator by 6.
   • Convert $\frac{5}{6}$ to $\frac{25}{30}$ by multiplying both the numerator and denominator by 5.

2. Now subtract the two fractions:

   $\frac{24}{30} - \frac{25}{30} = \frac{24 - 25}{30} = \frac{-1}{30}$

3. Substitute back into the original expression:

   $3 - \left(\frac{-1}{30}\right) = 3 + \frac{1}{30}$

4. Finally, write $3$ as $\frac{90}{30}$ and add the fractions:

   $\frac{90}{30} + \frac{1}{30} = \frac{91}{30}$

Thus, the result is:

$\frac{91}{30}$

Would you like further clarification or details on any step?

Here are five related questions you might find helpful:

1. How do you find the least common denominator between two fractions?
2. How do you add or subtract fractions with different denominators?
3. What is the process for converting improper fractions to mixed numbers?
4. How would you handle this problem if it included variables?
5. Can you explain how to handle more complex expressions with multiple terms?

Tip: When adding or subtracting fractions, always start by finding the least common denominator to simplify calculations.