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

xy − w
xy + w
=

1 answer

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 \(\boxed{5}\).