# How do you simplify (5-i)/(5+i)?

Jan 5, 2017

$\frac{12}{13} - \frac{5}{13} i$

#### Explanation:

You can multiply both the terms of the fraction by

$5 - i$

and get:

${\left(5 - i\right)}^{2} / \left(\left(5 + i\right) \left(5 - i\right)\right)$

that's:

$\frac{25 - 10 i + {i}^{2}}{25 - {i}^{2}}$

Then, since

${i}^{2} = - 1$, you get:

$\frac{25 - 10 i - 1}{25 + 1}$

$\frac{24 - 10 i}{26}$

${\cancel{24}}^{12} / {\cancel{26}}^{13} - {\cancel{10}}^{5} / {\cancel{26}}^{13} i$

$\frac{12}{13} - \frac{5}{13} i$