# How do you write the mixed expression n^2+(n-1)/(n+4) as a rational expression?

May 2, 2017

$\frac{{n}^{3} + 4 {n}^{2} + n - 1}{n + 4}$

#### Explanation:

A rational expression is an algebraic fraction with a $\textcolor{b l u e}{\text{polynomial}}$ on the numerator and denominator.

$\text{before adding the mixed expression we require the terms}$

$\text{to have a "color(blue)"common denominator}$

$\text{multiply " n^2" by } \frac{n + 4}{n + 4}$

$\Rightarrow \frac{{n}^{2} \left(n + 4\right)}{n + 4} + \frac{n - 1}{n + 4}$

Now the 2 terms have a common denominator we can add the numerators leaving the denominator as it is.

$\Rightarrow \frac{{n}^{3} + 4 {n}^{2} + n - 1}{n + 4} \leftarrow \textcolor{red}{\text{ rational expression}}$