# How do you combine n/(5-n)+(2n-5)/(n-5)?

Feb 10, 2017

$1$

#### Explanation:

Using an example. Suppose we had -5

Another way of writing this is: $- \left(+ 5\right)$

So we can 'force' a change in sign so that both denominators are the same:

Write $\frac{n}{5 - n} \text{ as } \frac{n}{- \left(- 5 + n\right)}$

Just changing the order we have: $\frac{n}{- \left(- 5 + n\right)} \to - \frac{n}{n - 5}$

So write: $\textcolor{red}{\frac{n}{5 - n}} \textcolor{g r e e n}{+ \frac{2 n - 5}{n - 5}} \text{ as } \textcolor{g r e e n}{\frac{2 n - 5}{n - 5}} \textcolor{red}{- \frac{n}{n - 5}}$

$= \frac{2 n - 5 - n}{n - 5} \text{ " =" " (n-5)/(n-5)" "=" } 1$