Question

Evaluate the expression for x = –1, y = 8, and z = –16. Simplify your answer.

xz
xy + y − z
=

Answer 1

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.

1. Substitute the values into the expression:
\[
xz = (-1)(-16) = 16
\]
\[
xy + y - z = (-1)(8) + 8 - (-16)
\]

2. Calculate \( xy + y - z \):
\[
(-1)(8) = -8
\]
Now, plug that into the expression:
\[
-8 + 8 - (-16)
\]

Simplifying further:
\[
-8 + 8 + 16 = 0 + 16 = 16
\]

3. Now we have that \( xz = 16 \) and \( xy + y - z = 16 \).

4. Substitute these values back into the original expression:
\[
\frac{xz}{xy + y - z} = \frac{16}{16} = 1
\]

Thus, the simplified answer is:
\[
\boxed{1}
\]