## College Algebra (6th Edition)

$2i-1$
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 $-1$. $\frac{5i}{2-i}$ $\frac{5i}{2-i}(\frac{2+i}{2+i})$ $\frac{10i+5i^2}{4-2i+2i-i^2}$ $\frac{10i+5(-1)}{4-(-1)}$ $\frac{10i-5}{5}$ $\frac{5(2i-1)}{5}$ $2i-1$