simplify 5/(2+i)

Solution

simplify

\frac{5}{2 + i}

2 - i

Solution steps

\frac{5}{2 + i}

Multiply by the conjugate

\frac{2 - i}{2 - i}

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

Simplify

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

= \frac{10 - 5 i}{5}

Apply the fraction rule:

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

= \frac{10}{5} + \frac{- 5}{5} i

Simplify

\frac{10}{5} + \frac{- 5}{5} i : 2 - i

= 2 - i

x (x + 1) (x - 2)

(7 + 3) (7 - 3)

\frac{8 x ^{2} - 40 x}{2 x ^{2}}

\frac{4 x ^{2} + 16 x}{x ^{2} - 16}

- 9 + 1