To evaluate the expression \(\frac{u - v}{u + v}\) using \(u = -15\) and \(v = 9\), let's substitute the values of \(u\) and \(v\) into the expression.
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Substitute \(u\) and \(v\), \[ \frac{-15 - 9}{-15 + 9} \]
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Simplify the numerator and the denominator:
- For the numerator: \[ -15 - 9 = -24 \]
- For the denominator: \[ -15 + 9 = -6 \]
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Now we have: \[ \frac{-24}{-6} \]
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Simplify the fraction: \[ \frac{-24}{-6} = 4 \]
Thus, the simplified answer is: \[ \boxed{4} \]