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Let's solve the given expression step-by-step:

The expression is:

\[
\left[ \frac{3}{4} + \left(2 - \frac{1}{5}\right) - \frac{7}{10} \right] \cdot \left(1 \div \frac{9}{10}\right) + 3
\]

### Step 1: Simplify inside the brackets and parentheses

1. **Inside the first square bracket:**  
   \[
   \frac{3}{4} + \left(2 - \frac{1}{5}\right) - \frac{7}{10}
   \]
   
   - Calculate \(2 - \frac{1}{5}\):
     \[
     2 - \frac{1}{5} = \frac{10}{5} - \frac{1}{5} = \frac{9}{5}
     \]

   - Now we have:
     \[
     \frac{3}{4} + \frac{9}{5} - \frac{7}{10}
     \]

   - Find a common denominator for the fractions. The least common multiple of 4, 5, and 10 is 20.
   
   - Convert each fraction to have a denominator of 20:
     \[
     \frac{3}{4} = \frac{15}{20}, \quad \frac{9}{5} = \frac{36}{20}, \quad \frac{7}{10} = \frac{14}{20}
     \]

   - Add and subtract the fractions:
     \[
     \frac{15}{20} + \frac{36}{20} - \frac{14}{20} = \frac{15 + 36 - 14}{20} = \frac{37}{20}
     \]

2. **Inside the second parenthesis:**
   \[
   1 \div \frac{9}{10}
   \]

   - Dividing by a fraction is the same as multiplying by its reciprocal:
     \[
     1 \div \frac{9}{10} = 1 \times \frac{10}{9} = \frac{10}{9}
     \]

### Step 2: Combine the simplified terms

Now, the expression is:
\[
\frac{37}{20} \times \frac{10}{9} + 3
\]

### Step 3: Perform the multiplication

- Multiply the fractions:
  \[
  \frac{37}{20} \times \frac{10}{9} = \frac{37 \times 10}{20 \times 9} = \frac{370}{180}
  \]

- Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 10:
  \[
  \frac{370 \div 10}{180 \div 10} = \frac{37}{18}
  \]

### Step 4: Add the result to 3

- Convert 3 to a fraction with a denominator of 18:
  \[
  3 = \frac{54}{18}
  \]

- Add the fractions:
  \[
  \frac{37}{18} + \frac{54}{18} = \frac{91}{18}
  \]

### Step 5: Simplify or convert to a mixed number (if necessary)

- \(\frac{91}{18}\) can be converted to a mixed number:
  \[
  \frac{91}{18} = 5 \frac{1}{18}
  \]

### Final Answer

\[
5 \frac{1}{18}
\]

Or, as an improper fraction:

\[
\frac{91}{18}
\]

Would you like more details on any step, or do you have any questions?

### Related Questions

1. How do you find the least common multiple (LCM) of a set of numbers?
2. What is the process of converting improper fractions to mixed numbers?
3. Why is multiplying by a reciprocal the same as dividing by a fraction?
4. How do you simplify fractions by finding the greatest common divisor (GCD)?
5. What are some strategies for working with fractions involving multiple operations?

### Tip

When working with expressions that have multiple fractions and operations, always simplify step-by-step and convert fractions to a common denominator where necessary to make calculations easier.

Learn how to solve the given expression step-by-step, involving fractions. This problem covers key concepts such as operations with fractions, converting between improper fractions and mixed numbers, and simplifying complex expressions. Suitable for students in Grades 6-8.

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