It seems that the extraction of the mathematical content from the image was unsuccessful. I will transcribe the equation manually and proceed with solving it.

The expression appears to be:

$\left( \frac{3}{5} \right)^2 + \frac{1}{5} - \left( \frac{1}{7} - \frac{3}{4} \right) + \left( \frac{-1}{2} \right)^2 = ?$

Now, let's go step by step to solve it:

Step 1: Simplify each term

1. $\left( \frac{3}{5} \right)^2 = \frac{9}{25}$
2. $\frac{1}{5}$ stays as is.
3. $\frac{1}{7} - \frac{3}{4}$ needs a common denominator, which is 28: $\frac{1}{7} = \frac{4}{28}, \quad \frac{3}{4} = \frac{21}{28}$ So, $\frac{1}{7} - \frac{3}{4} = \frac{4}{28} - \frac{21}{28} = \frac{-17}{28}$.
4. $\left( \frac{-1}{2} \right)^2 = \frac{1}{4} = \frac{7}{28}$ (converted to have a denominator of 28 for later steps).

Step 2: Substitute into the expression

$\frac{9}{25} + \frac{1}{5} - \left( \frac{-17}{28} \right) + \frac{7}{28}$

I will now compute the result.The result of the expression is:

$\frac{248}{175}$

This can also be written as approximately 1.417.

Would you like more details on any part of the process, or further explanations? Here are a few related questions:

1. How do you handle fractions with different denominators when adding or subtracting?
2. What is the general method for squaring fractions?
3. Why did we use a common denominator in the subtraction step?
4. How can we convert improper fractions to mixed numbers?
5. What are some techniques to simplify expressions involving fractions?

Tip: When working with fractions, it's often easier to simplify the problem by converting to a common denominator early in the calculation.