To simplify the expressions given in the image, we can proceed step-by-step for each expression one by one:

### 6)
\[
\frac{x - y}{xy - y^2} - \frac{x}{x^2 - xy} \cdot \frac{x^2y + xy^2}{x^2 - y} \cdot \frac{13}{3y}
\]
First, rewrite and factor where needed. The simplification involves common factors.

### 7)
\[
\left(1 + \frac{x}{y} + \frac{x^2}{y^2}\right) \cdot \left(\frac{x}{y} - 1\right) \cdot \frac{y^2}{x^3 - y^3}
\]
This can be simplified by factoring out common elements, particularly identifying differences of cubes.

### 8)
\[
\frac{a - b}{\frac{a + b}{a - b}} \cdot \left(\frac{a^2 + b^2}{2ab} + 1\right)
\]
You can simplify \(\frac{a - b}{\left(\frac{a + b}{a - b}\right)}\) and compute the second term.

### 9)
\[
\left(\frac{a^2}{b}\cdot \frac{b^2}{a}\right) \cdot \left(\frac{a + b}{a^2 + ab + b^2} + \frac{1}{a - b}\right)
\]
Simplify by substituting with \(k = ab\) to factor terms directly if applicable.

### 10)
\[
\left(\frac{a}{ab - b^2} - \frac{2a - b^2}{a^2 - ab}\right) : \left(\frac{a^2 - 2ab + b^2}{a^2b - ab^2}\right)
\]
Here, combine fractions and simplify by finding a common denominator.

### General Steps:
1. **Factor where possible:** Identify values that can be factored, such as differences of squares or cubes.
2. **Common Denominator:** When subtracting or adding fractions, find a common denominator.
3. **Multiply Out:** After multiplication, combine like terms.
4. **Cancel Common Factors:** If terms are present in the numerator and denominator, they can be canceled.

Once you've followed through the algebra, you should arrive at each simplified expression. If specific values or further steps are needed, please provide the intermediate results, and I can help refine them!