$\frac{3 + 5 i}{2 - i} - \frac{4 - 3 i}{3 - 2 i} = \frac{174 i - 77}{65}$

Explanation

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$\frac{3 + 5 i}{2 - i} - \frac{4 - 3 i}{3 - 2 i} \overset{◯}{1} \frac{1 + 13 i}{5} - \frac{18 - i}{13} \overset{◯}{2} \frac{174 i - 77}{65}$
①	Divide $3 + 5 i$ by $2 - i$ to get $\frac{1 + 13 i}{5}$ . ( view steps )Divide $4 - 3 i$ by $3 - 2 i$ to get $\frac{18 - i}{13}$ . ( view steps )
②	Subtract $\frac{18 - i}{13}$ from $\frac{1 + 13 i}{5}$ to get $\frac{174 i - 77}{65}$ . To subtract raitonal expressions, both fractions must have the same denominator. We can create a common denominator by multiplying the first fraction by $13$ and the second by $5$ . $\frac{1 + 13 i}{5} - \frac{18 - i}{13} = \frac{( 1 + 13 i ) \cdot 13}{5 \cdot 13} - \frac{( 18 - i ) \cdot 5}{13 \cdot 5} = = \frac{13 + 169 i}{65} - \frac{90 - 5 i}{65} = \frac{13 + 169 i - ( 90 - 5 i )}{65} = = \frac{174 i - 77}{65}$

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2−i3+5i​−3−2i4−3i​=65174i−77​

$\frac{3 + 5 i}{2 - i} - \frac{4 - 3 i}{3 - 2 i} = \frac{174 i - 77}{65}$