Multiply $ \dfrac{1}{83} $ by $ x-64 $ to get $ \dfrac{ x-64 }{ 83 } $.

Step 1: Write $ x-64 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{83} \cdot x-64 & \xlongequal{\text{Step 1}} \frac{1}{83} \cdot \frac{x-64}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( x-64 \right) }{ 83 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x-64 }{ 83 } \end{aligned} $$

Add $ \dfrac{x-64}{83} $ and $ 82 $ to get $ \dfrac{ \color{purple}{ x+6742 } }{ 83 }$.

Step 1: Write $ 82 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{83}$.

$$ \begin{aligned} \frac{x-64}{83} +82 & \xlongequal{\text{Step 1}} \frac{x-64}{83} + \frac{82}{\color{red}{1}} = \frac{ x-64 }{ 83 } + \frac{ 82 \cdot \color{blue}{ 83 }}{ 1 \cdot \color{blue}{ 83 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x-64 } }{ 83 } + \frac{ \color{purple}{ 6806 } }{ 83 }=\frac{ \color{purple}{ x+6742 } }{ 83 } \end{aligned} $$