If `xy+z=y`, what is x in terms of y and z?

Options

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

Answer

To solve the equation \( xy + z = y \) for \( x \) in terms of \( y \) and \( z \), we can follow these steps:

### Step 1: Write down the original equation
We start with the equation:
\[ xy + z = y \]

### Step 2: Subtract \( z \) from both sides
To isolate the term involving \( x \), we subtract \( z \) from both sides:
\[ xy + z - z = y - z \]
This simplifies to:
\[ xy = y - z \]

### Step 3: Divide both sides by \( y \)
Next, we divide both sides of the equation by \( y \) to solve for \( x \):
\[ \frac{xy}{y} = \frac{y - z}{y} \]
This simplifies to:
\[ x = \frac{y - z}{y} \]

### Final Answer
Thus, \( x \) in terms of \( y \) and \( z \) is:
\[ x = \frac{y - z}{y} \]

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