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The document you uploaded includes algebraic problems focusing on partial fraction decomposition, specifically for both **improper fractions** and different **cases** of partial fractions.

Here are a few examples from the document:

1. Decompose the fraction:  
   \[
   \frac{1}{4x^2 - x}
   \]
   
2. Decompose the fraction:  
   \[
   \frac{3x^2 + 3x - 12}{6x^3 + 5x^2 - 6x}
   \]

3. Solve the improper function:  
   \[
   \frac{2x^3 + 4}{x^2 - 4}
   \]

Additionally, more complex cases are included, like:

4. Decompose the fraction:  
   \[
   \frac{4x^3 - 8x^2 - 10x + 30}{2x^2 + x - 6}
   \]

5. Decompose the fraction:  
   \[
   \frac{x^2 + x + 1}{x^4 - x^3}
   \]

These problems require breaking down the given rational expressions into simpler fractions using partial fraction decomposition methods, covering both proper and improper rational expressions.

Would you like help with solving any specific problem from this list?

Here are 5 related questions that expand on this topic:
1. What are the steps for partial fraction decomposition of proper rational expressions?
2. How do you approach the decomposition of improper rational functions?
3. How do you handle repeated linear factors in the denominator during partial fraction decomposition?
4. What are some common mistakes when solving improper fraction decomposition?
5. How do you use partial fraction decomposition in integral calculus?

**Tip**: Always check if the degree of the numerator is greater than or equal to the denominator; if so, perform polynomial division before decomposing.

The document you uploaded includes algebraic problems focusing on partial fraction decomposition, specifically for both improper fractions and different cases of partial fractions.

Explore how to decompose improper fractions and handle complex cases of partial fraction decomposition with detailed examples from algebra. This guide includes polynomial division and breaking down rational expressions into simpler parts, suitable for Grades 10-12.

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