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The expression you provided is:

\[
\frac{\frac{-3}{x} + 6}{-3 - \frac{x}{y}}
\]

Let's simplify it step by step.

### Step 1: Simplify the numerator
The numerator is:
\[
\frac{-3}{x} + 6
\]
We can rewrite 6 as \(\frac{6x}{x}\) to have a common denominator:
\[
\frac{-3}{x} + \frac{6x}{x} = \frac{-3 + 6x}{x}
\]
Thus, the numerator becomes:
\[
\frac{6x - 3}{x}
\]

### Step 2: Simplify the denominator
The denominator is:
\[
-3 - \frac{x}{y}
\]
To combine these terms, we can rewrite \(-3\) as \(\frac{-3y}{y}\):
\[
\frac{-3y}{y} - \frac{x}{y} = \frac{-3y - x}{y}
\]
So the denominator becomes:
\[
\frac{-3y - x}{y}
\]

### Step 3: Combine numerator and denominator
Now we have the following expression:
\[
\frac{\frac{6x - 3}{x}}{\frac{-3y - x}{y}}
\]
To simplify this complex fraction, multiply by the reciprocal of the denominator:
\[
\frac{6x - 3}{x} \times \frac{y}{-3y - x}
\]
This simplifies to:
\[
\frac{(6x - 3) \cdot y}{x \cdot (-3y - x)}
\]

### Final simplified expression:
The simplified form of the given expression is:
\[
\frac{y(6x - 3)}{x(-3y - x)}
\]

Would you like more details on a specific step or have further questions?

Here are five related questions you might consider:
1. How can you simplify complex fractions in other cases?
2. What are the rules for multiplying fractions with variables?
3. How can you factor expressions to simplify them further?
4. How does changing variables affect the simplification process?
5. What strategies are useful for combining fractions with different denominators?

**Tip:** Always look for opportunities to factor terms to make simplifications easier.

Simplify the expression \(\frac{\frac{-3}{x} + 6}{-3 - \frac{x}{y}}\).

Learn how to simplify the complex fraction \(\frac{\frac{-3}{x} + 6}{-3 - \frac{x}{y}}\) with a detailed step-by-step solution. This algebra problem covers important concepts such as fraction addition, multiplication, and simplification. Suitable for students in Grades 9-12.

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