Add $x^2-2x$ and $ \dfrac{5}{9} $ to get $ \dfrac{ \color{purple}{ 9x^2-18x+5 } }{ 9 }$.

Step 1: Write $ x^2-2x $ 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 $\color{blue}{ 9 }$.

$$ \begin{aligned} x^2-2x+ \frac{5}{9} & \xlongequal{\text{Step 1}} \frac{x^2-2x}{\color{red}{1}} + \frac{5}{9} = \frac{ \left( x^2-2x \right) \cdot \color{blue}{ 9 }}{ 1 \cdot \color{blue}{ 9 }} + \frac{ 5 }{ 9 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9x^2-18x } }{ 9 } + \frac{ \color{purple}{ 5 } }{ 9 }=\frac{ \color{purple}{ 9x^2-18x+5 } }{ 9 } \end{aligned} $$