What is (2-i)/(3+i)-(5+2i)+3/(2-i) ?

The solution to (2-i)/(3+i)-(5+2i)+3/(2-i) is -33/10-19/10 i

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simplify (2-i)/(3+i)-(5+2i)+3/(2-i)

simplify

\frac{2 - i}{3 + i} - (5 + 2 i) + \frac{3}{2 - i}

- \frac{33}{10} - \frac{19}{10} i

Solution steps

\frac{2 - i}{3 + i} - (5 + 2 i) + \frac{3}{2 - i}

\frac{2 - i}{3 + i} = \frac{1 - i}{2}

- (5 + 2 i) = - 5 - 2 i

\frac{3}{2 - i} = \frac{6 + 3 i}{5}

= \frac{1 - i}{2} - 5 - 2 i + \frac{6 + 3 i}{5}

Join

\frac{1 - i}{2} - 5 - 2 i + \frac{6 + 3 i}{5} : \frac{- 19 i - 33}{10}

= \frac{- 19 i - 33}{10}

Rewrite in standard complex form:

- \frac{33}{10} - \frac{19}{10} i

= - \frac{33}{10} - \frac{19}{10} i

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What is (2-i)/(3+i)-(5+2i)+3/(2-i) ?
The solution to (2-i)/(3+i)-(5+2i)+3/(2-i) is -33/10-19/10 i