Add $ \dfrac{9}{10x} $ and $ \dfrac{1}{x} $ to get $ \dfrac{ \color{purple}{ 19x } }{ 10x^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}{ x }$ and the second by $\color{blue}{ 10x }$.

$$ \begin{aligned} \frac{9}{10x} + \frac{1}{x} & = \frac{ 9 \cdot \color{blue}{ x }}{ 10x \cdot \color{blue}{ x }} + \frac{ 1 \cdot \color{blue}{ 10x }}{ x \cdot \color{blue}{ 10x }} = \\[1ex] &=\frac{ \color{purple}{ 9x } }{ 10x^2 } + \frac{ \color{purple}{ 10x } }{ 10x^2 }=\frac{ \color{purple}{ 19x } }{ 10x^2 } \end{aligned} $$