The expression in the image appears to be:

$\frac{10}{\frac{2x - 3x - 2}{x - 2} - 2}$

Let's simplify this step by step.

1. Simplify the expression inside the fraction:

   $2x - 3x - 2 = -x - 2$

2. Substitute this into the expression:

   $\frac{10}{\frac{-x - 2}{x - 2} - 2}$

3. Simplify the fraction inside the denominator:

   $\frac{-x - 2}{x - 2} = \frac{-(x + 2)}{x - 2} = -\frac{x + 2}{x - 2}$

4. Substitute and simplify further:

   $\frac{10}{-\frac{x + 2}{x - 2} - 2}$

5. Combine the terms in the denominator:

   To combine the terms in the denominator, get a common denominator:

   $-\frac{x + 2}{x - 2} - 2 = -\frac{x + 2}{x - 2} - \frac{2(x - 2)}{x - 2} = \frac{-(x + 2) - 2(x - 2)}{x - 2}$

   Simplify the expression inside the numerator:

   $-(x + 2) - 2(x - 2) = -x - 2 - 2x + 4 = -3x + 2$

   So, the expression becomes:

   $\frac{10}{\frac{-3x + 2}{x - 2}} = 10 \times \frac{x - 2}{-3x + 2} = \frac{10(x - 2)}{-3x + 2}$

This is the simplified form of the given expression:

$\boxed{\frac{10(x - 2)}{-3x + 2}}$

Would you like more details or have any other questions?

Here are five related questions for further exploration:

1. How would the result change if the original expression had different coefficients?
2. Can this expression be factored further if specific values of $x$ are substituted?
3. What happens to the expression as $x$ approaches the value that makes the denominator zero?
4. How would the approach change if the expression was a polynomial of higher degree?
5. What is the general method for simplifying complex rational expressions like this?

Tip: Always check if the expression can be further simplified by factoring both the numerator and denominator.