simple (hopefully)

[red and white kop!]

i have to sketch the curve (x-2)/(x-3) and to do this i must first show that this term is identical to 1+ (1/x-3)
obviously this is very easy starting from 1+ (1/x-3) but from (x-2)/(x-3) i am at a loss as to the general method. i know this is a common method of simplifying functions in order to better sketch them, so i'd like to know exactly how it is done

 

[Deleted member 4993]

i have to sketch the curve (x-2)/(x-3) and to do this i must first show that this term is identical to 1+ (1/x-3)
obviously this is very easy starting from 1+ (1/x-3) but from (x-2)/(x-3) i am at a loss as to the general method. i know this is a common method of simplifying functions in order to better sketch them, so i'd like to know exactly how it is done

So you have a form:

\(\displaystyle \frac{N(umerator)}{D(enominator)} \, = \, \frac{(N \, - \, D) \, + \, D}{D} \, = \, \frac{(N \, - \, D)}{D} \, + \, 1\)

That's it...