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The problem requires you to add the two fractions:

\[
-\frac{11}{x - 2} + \frac{3 - 3x}{x}
\]

### Steps to simplify:

1. **Find a common denominator**: 
   The denominators are \( x - 2 \) and \( x \). The least common denominator (LCD) will be their product, \( (x - 2)(x) \).

2. **Rewrite both fractions with the common denominator**:

   \[
   -\frac{11}{x - 2} = \frac{-11x}{x(x - 2)}
   \]
   \[
   \frac{3 - 3x}{x} = \frac{(3 - 3x)(x - 2)}{x(x - 2)}
   \]

3. **Expand the second fraction**:
   \[
   (3 - 3x)(x - 2) = 3x - 6 - 3x^2 + 6x = -3x^2 + 9x - 6
   \]

   So, the second fraction becomes:
   \[
   \frac{-3x^2 + 9x - 6}{x(x - 2)}
   \]

4. **Add the two fractions**:
   Combine the two numerators over the common denominator:
   \[
   \frac{-11x + (-3x^2 + 9x - 6)}{x(x - 2)}
   \]
   Simplify the numerator:
   \[
   = \frac{-3x^2 - 2x - 6}{x(x - 2)}
   \]

5. **Final answer**:
   \[
   \boxed{\frac{-3x^2 - 2x - 6}{x(x - 2)}}
   \]

Would you like further explanation or have any specific questions?

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Here are five related questions:
1. How do you factor common terms from a polynomial?
2. What steps do you follow to find a common denominator?
3. Can this expression be simplified further?
4. How does the distributive property help in expanding fractions?
5. How would the solution change if one of the terms was multiplied by a constant?

**Tip**: When dealing with algebraic fractions, always look to simplify by factoring both numerators and denominators where possible.

Add: -11 / (x - 2) + (3 - 3x) / x. Simplify your answer as much as possible.

This guide explains how to add and simplify the rational expressions -11/(x - 2) + (3 - 3x)/x step-by-step. It covers finding the least common denominator (LCD), using the distributive property, and simplifying algebraic expressions. Ideal for students in Grades 8-10.

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