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

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

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

simplify

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

\frac{1}{3} + i

Solution steps

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

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

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

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

Join

\frac{3 - i}{5} - \frac{2 - 3 i}{3} + \frac{2 + i}{5} : \frac{5}{5} - \frac{2 - 3 i}{3}

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

Join

\frac{5}{5} - \frac{2 - 3 i}{3} : \frac{1 + 3 i}{3}

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

Rewrite in standard complex form:

\frac{1}{3} + i

= \frac{1}{3} + i

(x - 4) (x^{2} + 3 x - 5)

\frac{x}{x ^{2} - x - 2} - \frac{x}{x ^{2} + 4 x - 12} - \frac{2}{x ^{2} + 7 x + 6}

\frac{12 b}{6}

1 - 2 sin^{2} (x) + sin^{4} (x)

\frac{1}{4} 4^{44}

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