Add $ \dfrac{7}{x^2+14x+45} $ and $ \dfrac{x}{x+9} $ to get $ \dfrac{ \color{purple}{ x^2+5x+7 } }{ x^2+14x+45 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{x+5}$.

$$ \begin{aligned} \frac{7}{x^2+14x+45} + \frac{x}{x+9} & = \frac{ 7 }{ x^2+14x+45 } + \frac{ x \cdot \color{blue}{ \left( x+5 \right) }}{ \left( x+9 \right) \cdot \color{blue}{ \left( x+5 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 7 } }{ x^2+14x+45 } + \frac{ \color{purple}{ x^2+5x } }{ x^2+14x+45 }=\frac{ \color{purple}{ x^2+5x+7 } }{ x^2+14x+45 } \end{aligned} $$