7. If \( x=5, y=-1 \), and \( z=2 \), what is the value of \( \frac{y^{2}-\frac{x}{y}+x y z}{x y z} \) ? A. (O) -4

To find the value of the expression \( \frac{y^{2}-\frac{x}{y}+x y z}{x y z} \) with \( x=5, y=-1 \), and \( z=2 \), we will substitute these values into the expression. First, calculate each term separately: 1. Calculate \( y^2 \): \[ y^2 = (-1)^2 = 1 \] 2. Calculate \( \frac{x}{y} \): \[ \frac{x}{y} = \frac{5}{-1} = -5 \] 3. Calculate \( x y z \): \[ x y z = 5 \cdot (-1) \cdot 2 = -10 \] Now substitute these values back into the expression: \[ y^{2} - \frac{x}{y} + x y z = 1 - (-5) + (-10) \] This simplifies to: \[ 1 + 5 - 10 = 6 - 10 = -4 \] Putting everything back into the original fraction: \[ \frac{y^{2} - \frac{x}{y} + x y z}{x y z} = \frac{-4}{-10} = \frac{4}{10} = \frac{2}{5} \] Since the answer does not match the provided option (O) -4, let's see if we properly evaluated the expression. Upon completing these calculations: - For \( y^2 - \frac{x}{y} + x y z \), we indeed confirmed it equals -4. - Then computing \( \frac{-4}{-10} \) equals \( \frac{2}{5} \). Thus, the final value of \( \frac{y^{2}-\frac{x}{y}+x y z}{x y z} \) is \( \frac{2}{5} \). The provided option of (O) -4 is incorrect.