Add $ \dfrac{2x+7}{x-6} $ and $ \dfrac{2}{6-x} $ to get $ \dfrac{ \color{purple}{ -2x-5 } }{ -x+6 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ -1 }$.

$$ \begin{aligned} \frac{2x+7}{x-6} + \frac{2}{6-x} & = \frac{ \left( 2x+7 \right) \cdot \color{blue}{ \left( -1 \right) }}{ \left( x-6 \right) \cdot \color{blue}{ \left( -1 \right) }} + \frac{ 2 }{ 6-x } = \\[1ex] &=\frac{ \color{purple}{ -2x-7 } }{ -x+6 } + \frac{ \color{purple}{ 2 } }{ -x+6 }=\frac{ \color{purple}{ -2x-5 } }{ -x+6 } \end{aligned} $$