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Question

Answer

$$-\dfrac{-2+i}{5}+\dfrac{-4+i}{15}=\dfrac{-2i+2}{15}$$

Explanation
$$ \begin{aligned}-\frac{-2+i}{5}+\frac{-4+i}{15}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-2i+2}{15}\end{aligned} $$
①

Add $ \dfrac{2-i}{5} $ and $ \dfrac{-4+i}{15} $ to get $ \dfrac{ \color{purple}{ -2i+2 } }{ 15 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{2-i}{5} + \frac{-4+i}{15} & = \frac{ \left( 2-i \right) \cdot \color{blue}{ 3 }}{ 5 \cdot \color{blue}{ 3 }} + \frac{ -4+i }{ 15 } = \\[1ex] &=\frac{ \color{purple}{ 6-3i } }{ 15 } + \frac{ \color{purple}{ -4+i } }{ 15 }=\frac{ \color{purple}{ -2i+2 } }{ 15 } \end{aligned} $$
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