To evaluate the expression \( \frac{x^2 - y + z}{y + z} \) for \( x = 7 \), \( y = 12 \), and \( z = -17 \), we will first calculate the numerator and the denominator separately.
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Calculate \( x^2 - y + z \):
- First, calculate \( x^2 \): \[ x^2 = 7^2 = 49 \]
- Now substitute \( y \) and \( z \): \[ x^2 - y + z = 49 - 12 - 17 \]
- Calculate it step by step: \[ 49 - 12 = 37 \] \[ 37 - 17 = 20 \]
- So, \( x^2 - y + z = 20 \).
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Calculate \( y + z \):
- Now substitute \( y \) and \( z \): \[ y + z = 12 - 17 \]
- Calculate: \[ 12 - 17 = -5 \]
- So, \( y + z = -5 \).
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Now substitute back into the expression: \[ \frac{x^2 - y + z}{y + z} = \frac{20}{-5} \]
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Simplify: \[ \frac{20}{-5} = -4 \]
Thus, the final simplified answer is \( \boxed{-4} \).
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