To evaluate the expression \( \frac{uv + 6v + u}{3} \) for \( u = -1 \) and \( v = 5 \), we start by substituting the values of \( u \) and \( v \) into the expression.
First, we find \( uv \): \[ uv = (-1)(5) = -5 \]
Next, we calculate \( 6v \): \[ 6v = 6(5) = 30 \]
Then we simply have \( u \): \[ u = -1 \]
Now we can substitute \( uv \), \( 6v \), and \( u \) back into the expression: \[ uv + 6v + u = -5 + 30 - 1 \]
Calculating inside the parentheses: \[ -5 + 30 = 25 \] Then: \[ 25 - 1 = 24 \]
Now we substitute this result back into the original expression: \[ \frac{uv + 6v + u}{3} = \frac{24}{3} = 8 \]
Thus, the simplified answer is: \[ \boxed{8} \]