# How do you write the mixed expression r+1/(3r) as a rational expression?

Nov 15, 2017

$\frac{3 {r}^{2} + 1}{3 r}$

#### Explanation:

$\text{before we can add the 2 fractions we require them to}$
$\text{have a "color(blue)"common denominator}$

$\text{to obtain this multiply the numerator/denominator of}$

$r \text{ by } 3 r$

$\Rightarrow \frac{r}{1} \times \frac{3 r}{3 r} = \frac{3 {r}^{2}}{3 r}$

$\Rightarrow r + \frac{1}{3 r}$

$= \frac{3 {r}^{2}}{3 r} + \frac{1}{3 r} \leftarrow \textcolor{b l u e}{\text{common denominator of 3r}}$

$\text{add the numerators leaving the denominator as it is}$

$= \frac{3 {r}^{2} + 1}{3 r}$