If `z != 0` and `yz != 1` then `1/(y - 1/z)` =

Options

A. `(yz)/(zy - 1)`
B. `(y - z)/(z)`
C. `(yz - z)/(z - 1)`
D. `z/(zy - 1)`

Answer

To solve the expression \( \frac{1}{y - \frac{1}{z}} \), we will follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{1}{y - \frac{1}{z}} \]

### Step 2: Find a common denominator
To simplify the expression in the denominator, we need to find a common denominator for \( y \) and \( \frac{1}{z} \). The common denominator is \( z \). Thus, we can rewrite \( y \) as:
\[ y = \frac{y \cdot z}{z} \]
Now, substituting this back into the expression gives us:
\[ \frac{1}{\frac{y \cdot z}{z} - \frac{1}{z}} \]

### Step 3: Combine the fractions in the denominator
Now, we can combine the fractions in the denominator:
\[ \frac{1}{\frac{yz - 1}{z}} \]

### Step 4: Simplify the expression
Now, we can simplify the expression by multiplying by the reciprocal of the denominator:
\[ \frac{1}{\frac{yz - 1}{z}} = \frac{z}{yz - 1} \]

### Final Answer
Thus, the final simplified expression is:
\[ \frac{z}{yz - 1} \]

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