x/x-2y - 4y^2/2a+b

To simplify the expression \( \frac{x}{x - 2y} - \frac{4y^2}{2a + b} \), we first need to ensure that we have a common denominator if we want to combine the fractions.

1. Identify the denominators: The denominators are \( (x - 2y) \) and \( (2a + b) \).

2. Find a common denominator: The common denominator is \( (x - 2y)(2a + b) \).

3. Rewrite each fraction with the common denominator:

   • For the first fraction: \[ \frac{x}{x - 2y} \cdot \frac{2a + b}{2a + b} = \frac{x(2a + b)}{(x - 2y)(2a + b)} \]
   • For the second fraction: \[ \frac{4y^2}{2a + b} \cdot \frac{x - 2y}{x - 2y} = \frac{4y^2(x - 2y)}{(x - 2y)(2a + b)} \]

4. Combine the fractions: \[ \frac{x(2a + b) - 4y^2(x - 2y)}{(x - 2y)(2a + b)} \]

5. Distribute the terms in the numerator:

   • The expression becomes: \[ x(2a + b) - 4y^2x + 8y^3 \]
   • So, the combined fraction is: \[ \frac{x(2a + b) - 4y^2x + 8y^3}{(x - 2y)(2a + b)} \]

The expression simplifies to:

\[ \frac{x(2a + b - 4y^2) + 8y^3}{(x - 2y)(2a + b)} \]

This is a simplified form of the original expression.