https://file.aiquickdraw.com/mathbot/file/17257063803154nt4wiq1.jpg

The image contains the following mathematical expression:

\[
\left(\frac{1}{41} + \frac{1}{37} + \frac{1}{12} + \frac{1}{7}\right) - \left(\frac{36}{37} - \frac{11}{12} - \frac{40}{41} - \frac{6}{7}\right)
\]

Let's simplify this step by step.

### Step 1: Simplify the terms inside each group.
- For the first group: \(\frac{1}{41} + \frac{1}{37} + \frac{1}{12} + \frac{1}{7}\)
- For the second group: \(\frac{36}{37} - \frac{11}{12} - \frac{40}{41} - \frac{6}{7}\)

I will now calculate these values.Here are the results of the simplifications:

- The sum of the first group: \(\frac{1}{41} + \frac{1}{37} + \frac{1}{12} + \frac{1}{7} = \frac{35375}{127428}\)
- The simplified result of the second group: \(\frac{36}{37} - \frac{11}{12} - \frac{40}{41} - \frac{6}{7} = \frac{-226369}{127428}\)

Finally, subtracting the second group from the first gives:

\[
\frac{35375}{127428} - \frac{-226369}{127428} = \frac{76}{37}
\]

Thus, the simplified result of the entire expression is \(\frac{76}{37}\), which is approximately \(2.054\).

Would you like further details or have any questions?

### Related Questions:
1. How do you find the least common denominator for fractions?
2. What are the steps to subtract fractions with different denominators?
3. Can you explain how to convert an improper fraction to a mixed number?
4. What is the importance of simplifying fractions?
5. How would this expression change if one of the terms was negative in the first group?

### Tip: 
When dealing with fractions, always look for the least common denominator to simplify your calculations efficiently.

Simplify the expression (1/41 + 1/37 + 1/12 + 1/7) - (36/37 - 11/12 - 40/41 - 6/7).

Learn how to simplify the complex fraction expression (1/41 + 1/37 + 1/12 + 1/7) - (36/37 - 11/12 - 40/41 - 6/7). This step-by-step solution covers key concepts such as finding the least common denominator and applying fraction addition and subtraction. Suitable for Grades 6-8.

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