Given `x+ (1)/(y)=1 and y + (1)/(z)=1` find
xyz= ?

Answer

To solve the problem given the equations \( x + \frac{1}{y} = 1 \) and \( y + \frac{1}{z} = 1 \), we will find the value of \( xyz \).

### Step-by-Step Solution:

1. **Start with the first equation:**
\[ x + \frac{1}{y} = 1 \]
Rearranging this gives:
\[ x = 1 - \frac{1}{y} \]

2. **Substitute a value for \( y \):**
To solve for \( x \) and \( z \), we need to assume a value for \( y \). Let's assume:
\[ y = 2 \]
Now substitute \( y \) into the equation for \( x \):
\[ x = 1 - \frac{1}{2} \]
This simplifies to:
\[ x = 1 - 0.5 = \frac{1}{2} \]

3. **Use the second equation:**
Now substitute \( y = 2 \) into the second equation:
\[ y + \frac{1}{z} = 1 \]
This gives:
\[ 2 + \frac{1}{z} = 1 \]
Rearranging this gives:
\[ \frac{1}{z} = 1 - 2 = -1 \]
Therefore, solving for \( z \):
\[ z = -1 \]

4. **Now we have values for \( x \), \( y \), and \( z \):**
\[ x = \frac{1}{2}, \quad y = 2, \quad z = -1 \]

5. **Calculate \( xyz \):**
\[ xyz = \left(\frac{1}{2}\right) \times 2 \times (-1) \]
This simplifies to:
\[ xyz = 1 \times (-1) = -1 \]

### Final Answer:
\[ xyz = -1 \]