Use the distributive property.

Combine like terms

Multiply $ \dfrac{83}{10} $ by $ u $ to get $ \dfrac{ 83u }{ 10 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{83}{10} \cdot u & \xlongequal{\text{Step 1}} \frac{83}{10} \cdot \frac{u}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 83 \cdot u }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 83u }{ 10 } \end{aligned} $$

Add $ \dfrac{83u}{10} $ and $ 9 $ to get $ \dfrac{ \color{purple}{ 83u+90 } }{ 10 }$.

Step 1: Write $ 9 $ 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 $\color{blue}{10}$.

$$ \begin{aligned} \frac{83u}{10} +9 & \xlongequal{\text{Step 1}} \frac{83u}{10} + \frac{9}{\color{red}{1}} = \frac{ 83u }{ 10 } + \frac{ 9 \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 83u } }{ 10 } + \frac{ \color{purple}{ 90 } }{ 10 }=\frac{ \color{purple}{ 83u+90 } }{ 10 } \end{aligned} $$