The given expression is:

\[
\pi + \frac{3(\infty)}{\pi(\infty) - 3}
\]

### Step-by-step analysis:

1. The term \( \infty \) (infinity) is involved, which often leads to special considerations in mathematics, especially when operations like division or subtraction with infinity are involved.
2. Let's break down the fraction:

\[
\frac{3(\infty)}{\pi(\infty) - 3}
\]

In this case, we have infinity in both the numerator and the denominator.

- The numerator is \( 3(\infty) = \infty \).
- The denominator \( \pi(\infty) - 3 \) simplifies to \( \infty - 3 = \infty \), since subtracting any finite number from infinity still results in infinity.

So, the fraction becomes:

\[
\frac{\infty}{\infty}
\]

### Indeterminate Form:
The expression \( \frac{\infty}{\infty} \) is indeterminate, meaning it doesn't have a well-defined value without further context or limits. Without additional information, this expression is undefined.

Finally, adding \( \pi \) to an undefined or indeterminate value will still result in an undefined or indeterminate result.

### Conclusion:
The expression as it stands is **undefined** due to the \( \frac{\infty}{\infty} \) indeterminate form.

---

Would you like more details on handling limits and indeterminate forms, or do you have any further questions?

### Related Questions:
1. What are indeterminate forms in calculus, and how are they resolved?
2. How do you compute limits involving infinity in fractions?
3. What happens when you add a finite number to infinity?
4. Can \( \frac{\infty}{\infty} \) ever be evaluated in certain contexts?
5. How does L'Hopital's Rule help in dealing with indeterminate forms?

**Tip:** In calculus, indeterminate forms like \( \frac{0}{0} \) or \( \frac{\infty}{\infty} \) are often resolved using limit techniques like L'Hopital's Rule.

Explore the indeterminate form in the expression pi + 3(infinity)/pi(infinity)-3. This detailed breakdown covers key calculus concepts, including the indeterminate form \( \frac{\infty}{\infty} \) and L'Hopital's Rule. Perfect for advanced high school or college students studying calculus.

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