It seems like you're working with an expression involving trigonometric functions. Here's the expression you provided:

\[
\frac{\sin(x)}{\sin(x) - \cos(x)}
\]

Would you like to simplify it or solve for specific values of \(x\)?

### Simplification
The expression cannot be directly simplified any further without additional constraints or identities. However, we can explore some common trigonometric identities to manipulate the equation, but in this form, it's already fairly simplified.

### Solving for values
To solve for specific values of \(x\), we would typically set the equation equal to some value or use given conditions.

Let me know how you'd like to proceed or if you'd like to explore further options!

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Would you like:
1. To simplify further using specific trigonometric identities?
2. To solve the equation for specific values of \(x\)?
3. To analyze the behavior of the function graphically?
4. To explore limits of this expression as \(x \to 0\) or \(x \to \infty\)?
5. To find where the function is undefined or where its denominator is zero?

### Tip:
Always check if trigonometric expressions can be simplified using Pythagorean identities like \(\sin^2(x) + \cos^2(x) = 1\).

Explore the simplification and analysis of the trigonometric expression sin(x) / (sin(x) - cos(x)). Learn how to apply common trigonometric identities and solve for specific values of x. This content is suitable for students in Grades 10-12 studying advanced trigonometry.

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