If 2 is added to the numerator and denominator of a fraction it becomes and if 2 is subtracted from the numerator and denominator it becomes. Find the fraction.

Let's solve this step by step.

Let the original fraction be \( \frac{x}{y} \).

According to the first condition:
- If 2 is added to both the numerator and denominator, the fraction becomes \( \frac{x+2}{y+2} \).

According to the second condition:
- If 2 is subtracted from both the numerator and the denominator, the fraction becomes \( \frac{x-2}{y-2} \).

Now, we need more information about what the fraction "becomes" in both cases. Typically, these types of problems specify values for the new fractions (e.g., "it becomes 3/4" or "it becomes 1/2"). Could you please provide the missing values? 

Once I have that, I can help you find the fraction.

Would you like details on the process or have any further questions?

Here are 5 questions to expand on this:

1. What happens if different numbers are added to the numerator and denominator?
2. How do we handle more complex transformations of fractions?
3. What role does cross-multiplication play in solving these equations?
4. How would we solve a similar problem with three transformations?
5. How does this problem relate to rational functions in algebra?

**Tip:** When solving fraction problems, it's crucial to carefully set up the conditions as equations to avoid confusion later.

Learn how to solve a fraction problem where 2 is added and subtracted from both the numerator and denominator. This problem involves algebraic manipulation of fractions and cross-multiplication, suitable for students in Grades 8-10.

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