Add $ \dfrac{1}{x^2+2x} $ and $ \dfrac{x-1}{x} $ to get $ \dfrac{ \color{purple}{ x^3+x^2-x } }{ x^3+2x^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 $\color{blue}{ x^2+2x }$.

$$ \begin{aligned} \frac{1}{x^2+2x} + \frac{x-1}{x} & = \frac{ 1 \cdot \color{blue}{ x }}{ \left( x^2+2x \right) \cdot \color{blue}{ x }} + \frac{ \left( x-1 \right) \cdot \color{blue}{ \left( x^2+2x \right) }}{ x \cdot \color{blue}{ \left( x^2+2x \right) }} = \\[1ex] &=\frac{ \color{purple}{ x } }{ x^3+2x^2 } + \frac{ \color{purple}{ x^3+2x^2-x^2-2x } }{ x^3+2x^2 }=\frac{ \color{purple}{ x^3+x^2-x } }{ x^3+2x^2 } \end{aligned} $$