To evaluate the expression
\[ \frac{vw - w^2}{v} \]
for \( v = 9 \) and \( w = 6 \), we can first substitute the values into the expression and simplify step by step.
Substituting \( v \) and \( w \):
\[ \frac{(9)(6) - (6)^2}{9} \]
Calculating \( vw \) and \( w^2 \):
\[ vw = 9 \times 6 = 54 \] \[ w^2 = 6^2 = 36 \]
Now substitute these values back into the expression:
\[ \frac{54 - 36}{9} \]
Now, simplify the expression in the numerator:
\[ 54 - 36 = 18 \]
So the expression is now:
\[ \frac{18}{9} \]
Finally, calculate:
\[ \frac{18}{9} = 2 \]
Thus, the simplified answer is:
\[ \boxed{2} \]
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