$\frac{1 - 2 i}{2 + i} + \frac{4 - i}{3 + 2 i} = \frac{- 24 i + 10}{13}$

Explanation

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$\frac{1 - 2 i}{2 + i} + \frac{4 - i}{3 + 2 i} \overset{◯}{1} - i + \frac{10 - 11 i}{13} \overset{◯}{2} \frac{- 24 i + 10}{13}$
①	Divide $1 - 2 i$ by $2 + i$ to get $- i$ . ( view steps )Divide $4 - i$ by $3 + 2 i$ to get $\frac{10 - 11 i}{13}$ . ( view steps )
②	Add $- i$ and $\frac{10 - 11 i}{13}$ to get $\frac{- 24 i + 10}{13}$ . Step 1: Write $- i$ as a fraction by putting $1$ in the denominator. Step 2: To add raitonal expressions, both fractions must have the same denominator. We can create a common denominator by multiplying the first fraction by $13$ . $- i + \frac{10 - 11 i}{13} Step 1 \frac{- i}{1} + \frac{10 - 11 i}{13} = \frac{( - i ) \cdot 13}{1 \cdot 13} + \frac{10 - 11 i}{13} = Step 2 \frac{- 13 i}{13} + \frac{10 - 11 i}{13} = \frac{- 24 i + 10}{13}$

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2+i1−2i​+3+2i4−i​=13−24i+10​

$\frac{1 - 2 i}{2 + i} + \frac{4 - i}{3 + 2 i} = \frac{- 24 i + 10}{13}$