The image you provided contains a complex mathematical expression involving fractions, operations, and parentheses. Let's break it down step by step to simplify it.

To solve the expression, we will first simplify the components within the parentheses and fractions, and then proceed with the arithmetic operations according to the order of operations (PEMDAS).

Let me simplify this for you.

I'll begin by interpreting and solving the first part of the equation.Let’s start by analyzing the expression and solving it step by step.

The expression inside the brackets appears to be:

$\left[ \frac{3,2 + \frac{2}{7} \cdot 0,7}{0,6 - \frac{1}{3}} - \frac{(3,8 - \frac{2}{1} \cdot \frac{1}{6}) \cdot 1,4}{\frac{5}{15} - 3 \cdot \frac{1}{5}} \right] : \frac{4}{3} \cdot \frac{8}{8}$

Step 1: Handle each component of the expression.

First, let’s tackle the numerator and denominator within each fraction and simplify them.

1.1 Numerator for the first fraction:

$3,2 + \frac{2}{7} \cdot 0,7 = 3.2 + \left( \frac{2}{7} \cdot 0.7 \right)$ $\frac{2}{7} \cdot 0.7 = \frac{2 \cdot 0.7}{7} = \frac{1.4}{7} \approx 0.2$ $3.2 + 0.2 = 3.4$

1.2 Denominator for the first fraction:

$0,6 - \frac{1}{3} = 0.6 - 0.3333 = 0.2667$

Thus, the first fraction becomes: $\frac{3.4}{0.2667} \approx 12.75$

1.3 Now, for the second part of the numerator:

$(3.8 - \frac{2}{1} \cdot \frac{1}{6}) \cdot 1.4$ Simplify the expression inside the parentheses: $3.8 - \left( 2 \cdot \frac{1}{6} \right) = 3.8 - 0.3333 = 3.4667$ Now multiply by 1.4: $3.4667 \cdot 1.4 = 4.846$

1.4 Denominator for the second fraction:

$\frac{5}{15} - 3 \cdot \frac{1}{5} = \frac{1}{3} - 0.6 = -0.267$

Thus, the second fraction becomes: $\frac{4.846}{-0.267} \approx -18.15$

Step 2: Subtract the two results:

$12.75 - (-18.15) = 12.75 + 18.15 = 30.9$

Step 3: Final part of the expression:

$\frac{4}{3} \cdot \frac{8}{8} = \frac{4}{3}$

Thus, the entire expression becomes: $30.9 : \frac{4}{3} = 30.9 \times \frac{3}{4} = 23.175$

Final Answer:

The result of the expression is approximately $23.18$.

Would you like any further details on the steps, or have other questions on the process? Here's a list of related questions that might interest you:

1. How do I simplify complex fractions in expressions like this?
2. Can you explain the order of operations in more detail?
3. How do I handle operations inside parentheses more effectively?
4. What are some strategies for solving expressions with mixed fractions?
5. How do I approach solving equations involving multiple terms and fractions?

Tip: When simplifying expressions with fractions, it helps to convert them into decimals or use common denominators to make calculations easier.