# How do you simplify the rational expression: (m^2+10m+24)/(m+4)?

Apr 26, 2018

$m + 6$

#### Explanation:

$\frac{{m}^{2} + 10 m + 24}{m + 4}$

In simplifying algebraic fractions, always try to factorise first.
The quadratic trinomial has two factors:

$= \frac{\left(m + 6\right) \cancel{\left(m + 4\right)}}{\cancel{\left(m + 4\right)}}$

$= m + 6$

Apr 26, 2018

(m^2+10m+24)/(m+4)=color(blue)(m+6

#### Explanation:

Simplify:

$\frac{{m}^{2} + 10 m + 24}{m + 4}$

Factor the numerator.

$\frac{\left(m + 4\right) \left(m + 6\right)}{m + 4}$

Cancel $m + 4$ in the numerator and denominator.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(m + 4\right)}}} \left(m + 6\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{m + 4}}}}$

Simplify.

$m + 6$