What is 1/(2+i)-5/(1+4i) ?

The solution to 1/(2+i)-5/(1+4i) is 9/85+83/85 i

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simplify 1/(2+i)-5/(1+4i)

simplify

\frac{1}{2 + i} - \frac{5}{1 + 4 i}

\frac{9}{85} + \frac{83}{85} i

Solution steps

\frac{1}{2 + i} - \frac{5}{1 + 4 i}

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

\frac{5}{1 + 4 i} = \frac{5 - 20 i}{17}

= \frac{2 - i}{5} - \frac{5 - 20 i}{17}

Join

\frac{2 - i}{5} - \frac{5 - 20 i}{17} : \frac{83 i + 9}{85}

= \frac{83 i + 9}{85}

Rewrite in standard complex form:

\frac{9}{85} + \frac{83}{85} i

= \frac{9}{85} + \frac{83}{85} i

\frac{5}{8} + \frac{3}{8}

\frac{2 π}{\frac{x}{2}}

(a^{2} - 1)^{2}

(x - \frac{1}{2 x})^{2}

\frac{x - 5}{x ^{2} + 10 x + 25} \cdot \frac{x ^{2} + 2 x - 15}{x ^{2} - 25}