Use the distributive property.

Add $p$ and $ \dfrac{q}{9p-9q} $ to get $ \dfrac{ \color{purple}{ 9p^2-9pq+q } }{ 9p-9q }$.

Step 1: Write $ p $ 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 first fraction by $\color{blue}{ 9p-9q }$.

$$ \begin{aligned} p+ \frac{q}{9p-9q} & \xlongequal{\text{Step 1}} \frac{p}{\color{red}{1}} + \frac{q}{9p-9q} = \frac{ p \cdot \color{blue}{ \left( 9p-9q \right) }}{ 1 \cdot \color{blue}{ \left( 9p-9q \right) }} + \frac{ q }{ 9p-9q } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9p^2-9pq } }{ 9p-9q } + \frac{ \color{purple}{ q } }{ 9p-9q }=\frac{ \color{purple}{ 9p^2-9pq+q } }{ 9p-9q } \end{aligned} $$

Multiply $ \dfrac{9p^2-9pq+q}{9p-9q} $ by $ 9 $ to get $ \dfrac{ 81p^2-81pq+9q }{ 9p-9q } $.

Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{9p^2-9pq+q}{9p-9q} \cdot 9 & \xlongequal{\text{Step 1}} \frac{9p^2-9pq+q}{9p-9q} \cdot \frac{9}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 9p^2-9pq+q \right) \cdot 9 }{ \left( 9p-9q \right) \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 81p^2-81pq+9q }{ 9p-9q } \end{aligned} $$