What is 4/(2-3i)+2/(1+i) ?

The solution to 4/(2-3i)+2/(1+i) is 21/13-1/13 i

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simplify 4/(2-3i)+2/(1+i)

simplify

\frac{4}{2 - 3 i} + \frac{2}{1 + i}

\frac{21}{13} - \frac{1}{13} i

Solution steps

\frac{4}{2 - 3 i} + \frac{2}{1 + i}

\frac{4}{2 - 3 i} = \frac{8 + 12 i}{13}

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

= \frac{8 + 12 i}{13} + 1 - i

Join

\frac{8 + 12 i}{13} + 1 - i : \frac{- i + 21}{13}

= \frac{- i + 21}{13}

Rewrite in standard complex form:

\frac{21}{13} - \frac{1}{13} i

= \frac{21}{13} - \frac{1}{13} i

\frac{2 x - 1}{5 x + 2} - \frac{x + 5}{5 x + 2}

\frac{1}{2} x + \frac{3}{2}

8 5^{2} - 8 4^{2}

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

321