Simplify $ \dfrac{a^2+2a-15}{a-3} $ to $ a+5$.

Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{a-3}$.

$$ \begin{aligned} \frac{a^2+2a-15}{a-3} & =\frac{ \left( a+5 \right) \cdot \color{blue}{ \left( a-3 \right) }}{ 1 \cdot \color{blue}{ \left( a-3 \right) }} = \\[1ex] &= \frac{a+5}{1} =a+5 \end{aligned} $$

Multiply $a+5$ by $ \dfrac{2}{a^2-4} $ to get $ \dfrac{ 2a+10 }{ a^2-4 } $.

Step 1: Write $ a+5 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} a+5 \cdot \frac{2}{a^2-4} & \xlongequal{\text{Step 1}} \frac{a+5}{\color{red}{1}} \cdot \frac{2}{a^2-4} \xlongequal{\text{Step 2}} \frac{ \left( a+5 \right) \cdot 2 }{ 1 \cdot \left( a^2-4 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2a+10 }{ a^2-4 } \end{aligned} $$