# How do you divide (x^4+2x^2+2x-3)/(2x^2-x)?

Jan 21, 2016

Using polynomial long division (below)
$\frac{1}{2} {x}^{2} + \frac{1}{4} x + \frac{9}{8}$ with remainder $\frac{25 x + 24}{16 {x}^{2} - 8 x}$

#### Explanation:

Remember to allow for the (zero) ${x}^{3}$ term:

Note that the remainder $\frac{25}{8} x + 3$ (over $2 {x}^{2} - x$)
can be simplified as
$\textcolor{w h i t e}{\text{XXX}} \frac{25 x + 24}{16 {x}^{2} - 8 x}$ to avoid fractions of fractions.