Add $ \dfrac{9}{4x} $ and $ \dfrac{2}{3x} $ to get $ \dfrac{ \color{purple}{ 35x } }{ 12x^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}{ 3x }$ and the second by $\color{blue}{ 4x }$.

$$ \begin{aligned} \frac{9}{4x} + \frac{2}{3x} & = \frac{ 9 \cdot \color{blue}{ 3x }}{ 4x \cdot \color{blue}{ 3x }} + \frac{ 2 \cdot \color{blue}{ 4x }}{ 3x \cdot \color{blue}{ 4x }} = \\[1ex] &=\frac{ \color{purple}{ 27x } }{ 12x^2 } + \frac{ \color{purple}{ 8x } }{ 12x^2 }=\frac{ \color{purple}{ 35x } }{ 12x^2 } \end{aligned} $$