If `ynez`, then `(xy-zx)/(z-y)=`

Options

A. `-x`
B. `-1`
C. `1`
D. `x`

Explanation

To solve the expression \((xy - zx)/(z - y)\), we will simplify it step by step.

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

### Step 2: Factor out common terms in the numerator
In the numerator \(xy - zx\), we can factor out \(x\):
\[ xy - zx = x(y - z) \]
So, we can rewrite the expression as:
\[ \frac{x(y - z)}{z - y} \]

### Step 3: Use the property of subtraction
We know that \(y - z\) can be rewritten using the property of subtraction:
\[ y - z = -1(z - y) \]
Substituting this into our expression gives:
\[ \frac{x(-1(z - y))}{z - y} \]

### Step 4: Simplify the expression
Now, we can simplify the expression:
\[ \frac{-x(z - y)}{z - y} \]
Since \(z - y\) is in both the numerator and the denominator, and \(y \neq z\) (which means \(z - y \neq 0\)), we can cancel \(z - y\):
\[ -x \]

### Final Result
Thus, the simplified expression is:
\[ \frac{xy - zx}{z - y} = -x \]