Question

Evaluate the expression for w = 12, x = –6, and y = 3. Simplify your answer.

xy − w
xy + w
=

Answer 1

To evaluate the expression \(\frac{xy - w}{xy + w}\) given \(w = 12\), \(x = -6\), and \(y = 3\), we first need to calculate \(xy\).

1. Calculate \(xy\):
\[
xy = (-6)(3) = -18
\]

2. Substitute \(xy\) and \(w\) into the expression:
\[
\frac{xy - w}{xy + w} = \frac{-18 - 12}{-18 + 12}
\]

3. Simplify the numerator and denominator:
- Numerator:
\[
-18 - 12 = -30
\]
- Denominator:
\[
-18 + 12 = -6
\]

4. The expression now becomes:
\[
\frac{-30}{-6}
\]

5. Simplify the fraction:
\[
\frac{-30}{-6} = 5
\]

So, the simplified result of the expression \(\frac{xy - w}{xy + w}\) is \(\boxed{5}\).