Let's evaluate each expression in terms of whether it is rational or irrational, given that \( x \) and \( y \) are non-zero, rational numbers, and \( z \) is an irrational number.
1. **Expression: \( x + y \)**
- Since both \( x \) and \( y \) are rational numbers, their sum \( x + y \) is also a rational number.
- **Value: Rational**
2. **Expression: \( y + z \)**
- Here, \( y \) is a rational number and \( z \) is an irrational number. The sum of a rational number and an irrational number is always irrational.
- **Value: Irrational**
3. **Expression: \( xy \)**
- The product of two rational numbers \( x \) and \( y \) is also a rational number.
- **Value: Rational**
4. **Expression: \( xz \)**
- Here, \( x \) is a rational number and \( z \) is an irrational number. The product of a rational number and an irrational number is always irrational.
- **Value: Irrational**
Thus, the final classification of the values is:
| Expression | Value |
|------------|-----------|
| \( x + y \) | Rational |
| \( y + z \) | Irrational |
| \( xy \) | Rational |
| \( xz \) | Irrational |