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

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

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

simplify

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

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

Solution steps

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

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

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

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

Join

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

= \frac{i + 3}{2}

Rewrite in standard complex form:

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

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

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