https://file.aiquickdraw.com/mathbot/file/172673968919975yncu7z.jpg

The image shows a math problem in Indonesian that translates to:

"31. Determine the result of \(\frac{x-y}{4} - \frac{x+2y}{3}\)."

Let's solve this expression step-by-step.

1. **Find the Common Denominator:**
   The common denominator for 4 and 3 is 12.

2. **Rewrite Each Fraction:**
   \[
   \frac{x-y}{4} = \frac{3(x-y)}{12} = \frac{3x - 3y}{12}
   \]
   \[
   \frac{x+2y}{3} = \frac{4(x+2y)}{12} = \frac{4x + 8y}{12}
   \]

3. **Subtract the Fractions:**
   \[
   \frac{3x - 3y}{12} - \frac{4x + 8y}{12} = \frac{3x - 3y - (4x + 8y)}{12}
   \]
   Simplify inside the numerator:
   \[
   3x - 3y - 4x - 8y = -x - 11y
   \]

4. **Final Expression:**
   \[
   \frac{-x - 11y}{12} \text{ or } \frac{-(x + 11y)}{12}
   \]

So, the result is \(\frac{-(x + 11y)}{12}\).

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

### Related Questions:
1. How do you find the least common denominator for more complex fractions?
2. What is the method for simplifying complex rational expressions?
3. How can you check if two algebraic fractions are equivalent?
4. How do you handle subtraction when both numerator and denominator contain variables?
5. What are common mistakes to avoid when subtracting fractions with variables?

### Tip:
Always simplify your expressions step-by-step to avoid errors, especially when dealing with multiple variables.

Tentukan hasil dari \(\frac{x - y}{4} - \frac{x + 2y}{3}\)

Solve the algebraic expression \(\frac{x - y}{4} - \frac{x + 2y}{3}\) by finding a common denominator. This problem involves rational expressions, common denominators, and algebraic simplification. Suitable for Grades 7-9.

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