Add $ \dfrac{1}{4+4j} $ and $ \dfrac{1}{3-3j} $ to get $ \dfrac{ \color{purple}{ j+7 } }{ -12j^2+12 }$.

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}{ -3j+3 }$ and the second by $\color{blue}{ 4j+4 }$.

$$ \begin{aligned} \frac{1}{4+4j} + \frac{1}{3-3j} & = \frac{ 1 \cdot \color{blue}{ \left( -3j+3 \right) }}{ \left( 4+4j \right) \cdot \color{blue}{ \left( -3j+3 \right) }} + \frac{ 1 \cdot \color{blue}{ \left( 4j+4 \right) }}{ \left( 3-3j \right) \cdot \color{blue}{ \left( 4j+4 \right) }} = \\[1ex] &=\frac{ \color{purple}{ -3j+3 } }{ -\cancel{12j}+12-12j^2+ \cancel{12j} } + \frac{ \color{purple}{ 4j+4 } }{ -\cancel{12j}+12-12j^2+ \cancel{12j} } = \\[1ex] &=\frac{ \color{purple}{ j+7 } }{ -12j^2+12 } \end{aligned} $$