Multiply $ \dfrac{a^2-9a+8}{8} $ by $ \dfrac{1}{a-8} $ to get $ \dfrac{ a-1 }{ 8 } $.

Step 1: Factor numerators and denominators.

Step 2: Cancel common factors.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{a^2-9a+8}{8} \cdot \frac{1}{a-8} & \xlongequal{\text{Step 1}} \frac{ \left( a-1 \right) \cdot \color{blue}{ \left( a-8 \right) } }{ 8 } \cdot \frac{ 1 }{ 1 \cdot \color{blue}{ \left( a-8 \right) } } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ a-1 }{ 8 } \cdot \frac{ 1 }{ 1 } \xlongequal{\text{Step 3}} \frac{ \left( a-1 \right) \cdot 1 }{ 8 \cdot 1 } \xlongequal{\text{Step 4}} \frac{ a-1 }{ 8 } \end{aligned} $$