115/VB02. problem / Math - Solved Math Problems

MR-115 / 382a. problem

Simplify the following expression:

$\frac{2 + i}{2 - i} + \frac{2 - i}{2 + i}$

= \frac{{(2 + i)}^{2} + (2 - i)^{2}}{(2 - i) (2 + i)}

$= \frac{4 + 4 i + i^{2} + 4 - 4 i + i^{2}}{4 - i^{2}}$

$= \frac{4 - 1 + 4 - 1}{4 - (- 1)}$

$= \frac{6}{5}$

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