Question

How do you simplify `(x-2)/(x^2-8x+12 )`?

Answer 1

`1/(x-6)`

Explanation:

First, factor the denominator completely.

`(x-2)/(x^2-8x+12)`
`=(x-2)/((x-2)(x-6))`
`=cancel(x-2)/(cancel((x-2))(x-6))`
`color(blue)(=1/(x-6))`

WARNING: You can simplify this, however, take note that you have canceled out `(x-2)` in the denominator. If you are asked for the domain, make sure that `color(red)(x-2!=0)` or `color(red)(x!=2)`.