simplify (-2)/(5-i)

Solution

simplify

\frac{- 2}{5 - i}

- \frac{5}{13} - \frac{1}{13} i

Solution steps

\frac{- 2}{5 - i}

Multiply by the conjugate

\frac{5 + i}{5 + i}

= \frac{- 2 ( 5 + i )}{( 5 - i ) ( 5 + i )}

Simplify

\frac{- 2 ( 5 + i )}{( 5 - i ) ( 5 + i )} : \frac{- 10 - 2 i}{26}

= \frac{- 10 - 2 i}{26}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{- 10}{26} + \frac{- 2}{26} i

Simplify

\frac{- 10}{26} + \frac{- 2}{26} i : - \frac{5}{13} - \frac{1}{13} i

= - \frac{5}{13} - \frac{1}{13} i

\frac{5}{8} - \frac{5}{6}

(\frac{3 w x ^{- 4} y ^{5}}{w ^{- 3}})^{- 4}

- 2 < x < 3

1 + \frac{0.06}{365}

\frac{17}{11} = \frac{u}{13}