Add $ \dfrac{11}{r} $ and $ \dfrac{9}{2r} $ to get $ \dfrac{ \color{purple}{ 31r } }{ 2r^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}{ 2r }$ and the second by $\color{blue}{ r }$.

$$ \begin{aligned} \frac{11}{r} + \frac{9}{2r} & = \frac{ 11 \cdot \color{blue}{ 2r }}{ r \cdot \color{blue}{ 2r }} + \frac{ 9 \cdot \color{blue}{ r }}{ 2r \cdot \color{blue}{ r }} = \\[1ex] &=\frac{ \color{purple}{ 22r } }{ 2r^2 } + \frac{ \color{purple}{ 9r } }{ 2r^2 }=\frac{ \color{purple}{ 31r } }{ 2r^2 } \end{aligned} $$