To evaluate the expression \( \frac{xz}{xy + y - z} \) for \( x = -1 \), \( y = 8 \), and \( z = -16 \), we will substitute the values into the expression and simplify it step by step.
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Substitute the values into the expression: \[ xz = (-1)(-16) = 16 \] \[ xy + y - z = (-1)(8) + 8 - (-16) \]
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Calculate \( xy + y - z \): \[ (-1)(8) = -8 \] Now, plug that into the expression: \[ -8 + 8 - (-16) \]
Simplifying further: \[ -8 + 8 + 16 = 0 + 16 = 16 \]
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Now we have that \( xz = 16 \) and \( xy + y - z = 16 \).
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Substitute these values back into the original expression: \[ \frac{xz}{xy + y - z} = \frac{16}{16} = 1 \]
Thus, the simplified answer is: \[ \boxed{1} \]