Add $ \dfrac{x+3}{x+5} $ and $ \dfrac{6}{x^2+3x-10} $ to get $ \dfrac{ \color{purple}{ x^2+x } }{ x^2+3x-10 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ x-2 }$.

$$ \begin{aligned} \frac{x+3}{x+5} + \frac{6}{x^2+3x-10} & = \frac{ \left( x+3 \right) \cdot \color{blue}{ \left( x-2 \right) }}{ \left( x+5 \right) \cdot \color{blue}{ \left( x-2 \right) }} + \frac{ 6 }{ x^2+3x-10 } = \\[1ex] &=\frac{ \color{purple}{ x^2-2x+3x-6 } }{ x^2-2x+5x-10 } + \frac{ \color{purple}{ 6 } }{ x^2-2x+5x-10 } = \\[1ex] &=\frac{ \color{purple}{ x^2+x } }{ x^2+3x-10 } \end{aligned} $$