Answer
$2i-1$
Work Step by Step
Multiply the top and bottom of the term by the conjugate of the denominator. Then combine like terms and divide to simplify. Make sure to change $i^2$ to $-1$.
$\frac{5i}{2-i}$
$\frac{5i}{2-i}(\frac{2+i}{2+i})$
$\frac{10i+5i^2}{4-2i+2i-i^2}$
$\frac{10i+5(-1)}{4-(-1)}$
$\frac{10i-5}{5}$
$\frac{5(2i-1)}{5}$
$2i-1$
