Remove the parentheses by changing the sign of each term within them.

$$ - \left( -2+i \right) = 2-i $$

Remove the parentheses by changing the sign of each term within them.

$$ - \left( -2-i \right) = 2+i $$

Add $ \dfrac{00i}{s+2-i} $ and $ \dfrac{00i}{s+2+i} $ to get $ \dfrac{ \color{purple}{ 0 } }{ -i^2+s^2+4s+4 }$.

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}{ i+s+2 }$ and the second by $\color{blue}{ -i+s+2 }$.

$$ \begin{aligned} \frac{00i}{s+2-i} + \frac{00i}{s+2+i} & = \frac{ \left( 00i \right) \cdot \color{blue}{ \left( i+s+2 \right) }}{ \left( s+2-i \right) \cdot \color{blue}{ \left( i+s+2 \right) }} + \frac{ \left( 00i \right) \cdot \color{blue}{ \left( -i+s+2 \right) }}{ \left( s+2+i \right) \cdot \color{blue}{ \left( -i+s+2 \right) }} = \\[1ex] &=\frac{ \color{purple}{ \cancel{0i}0s00i^20is \cancel{0i} } }{ \cancel{is}+s^2+2s+ \cancel{2i}+2s+4-i^2 -\cancel{is} -\cancel{2i} } + \frac{ \color{purple}{ \cancel{0i}0s00i^20is \cancel{0i} } }{ \cancel{is}+s^2+2s+ \cancel{2i}+2s+4-i^2 -\cancel{is} -\cancel{2i} } = \\[1ex] &=\frac{ \color{purple}{ 0 } }{ -i^2+s^2+4s+4 } \end{aligned} $$