To evaluate the expression \( \frac{n^2 + np}{p^2} \) for \( n = -9 \) and \( p = 3 \), we can follow these steps:
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Calculate \( n^2 \): \[ n^2 = (-9)^2 = 81 \]
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Calculate \( np \): \[ np = (-9)(3) = -27 \]
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Substitute \( n^2 \) and \( np \) into the expression: \[ n^2 + np = 81 - 27 = 54 \]
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Calculate \( p^2 \): \[ p^2 = 3^2 = 9 \]
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Substitute \( n^2 + np \) and \( p^2 \) into the expression: \[ \frac{n^2 + np}{p^2} = \frac{54}{9} \]
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Simplify the fraction: \[ \frac{54}{9} = 6 \]
The final result is: \[ \boxed{6} \]