Question

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

Answer 1

`1`

Explanation:

Using an example. Suppose we had -5

Another way of writing this is: `-(+5)`

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

Write `n/(5-n)" as "n/(-(-5+n))`

Just changing the order we have: `n/(-(-5+n)) -> - n/(n-5)`

So write: `color(red)(n/(5-n))color(green)(+(2n-5)/(n-5))" as "color(green)((2n-5)/(n-5))color(red)( - n/(n-5))`

`=(2n-5-n)/(n-5)" " =" " (n-5)/(n-5)" "=" "1`