The expression $\frac{4}{5} - \frac{3}{0}$ is undefined due to division by zero. Division by zero is mathematically impossible because there is no number that, when multiplied by zero, will give a non-zero number. In this case, the term $\frac{3}{0}$ cannot be evaluated, making the entire expression undefined.

Would you like to explore more about why division by zero is undefined or have any other questions? Here are some related topics you might find interesting:

1. What happens when we try to divide by zero in algebraic expressions?
2. How do limits handle division by zero in calculus?
3. Can zero appear in the denominator of a fraction in different mathematical systems?
4. How do we simplify expressions with indeterminate forms like $\frac{0}{0}$?
5. What are some real-world examples where division by zero might come up?

Tip: In algebra and calculus, it's crucial to avoid division by zero as it leads to undefined or indeterminate results. Always check the denominators!