# How do you simplify n/(2n+10)+1/(n^2-25)?

Jul 3, 2017

$\frac{{n}^{2} - 5 n + 2}{2 \left(n - 5\right) \left(n + 5\right)}$

#### Explanation:

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

$\text{first factorise the denominators}$

$\Rightarrow \frac{n}{2 \left(n + 5\right)} + \frac{1}{\left(n - 5\right) \left(n + 5\right)} \leftarrow \textcolor{b l u e}{\text{ difference of squares}}$

$\text{multiply the numerator/denominator of the fraction on the }$
$\text{ left by } \left(n - 5\right)$

$\text{multiply the numerator/denominator of the fraction on the}$
$\text{right by } 2$

$\Rightarrow \frac{n \left(n - 5\right)}{2 \left(n + 5\right) \left(n - 5\right)} + \frac{2}{2 \left(n + 5\right) \left(n - 5\right)}$

$\text{now the denominators are common we can add the numerators}$
$\text{leaving the denominator as it is.}$

$\Rightarrow \frac{{n}^{2} - 5 n + 2}{2 \left(n + 5\right) \left(n - 5\right)}$

$= \frac{{n}^{2} - 5 n + 2}{2 \left(n + 5\right) \left(n - 5\right)}$