Answer
$-1+2i$
Work Step by Step
Rationalize the denominator by multiplying the conjugate of the denominator, which is $2+i$, to both the numerator and the denominator to obtain:
$=\dfrac{5i(2+i)}{(2-i)(2+i)}
\\=\dfrac{10i+5i^2}{(2-i)(2+i)}$
Use the rule $(a-b)(a+b) = a^2-b^2$ to obtain:
$=\dfrac{10i+5i^2}{2^2-i^2}
\\=\dfrac{10i+5i^2}{4-i^2}$
Use the fact that $i^2=-1$ to obtain:
$=\dfrac{10i+5(-1)}{4-(-1)}
\\=\dfrac{10i-5}{4+1}
\\=\dfrac{-5+10i}{5}
\\=\dfrac{-5}{5} + \dfrac{10}{5}i
\\=-1+2i$
