Question

How can you evaluate `(x-2)/(x-6) - (x+2)/(6-x)`?

Answer 1

`(x-2)/(x-6) - (x+2)/(6-x) = (2x)/(x-6)`

Explanation:

`(x+2)/(6-x) = (x+2)/((-1)(x-6)) = -(x+2)/(x-6)`

So
`(x-2)/(x-6) - (x+2)/(6-x)`

`color(white)("XXXX")` `= (x-2)/(x-6) - (-1)(x+2)/(x-6)`

`color(white)("XXXX")` `= (x-2)/(x-6) +(x+2)/(x-6)`

and since, in general `a/d + b/d = (a+b)/d`

`color(white)("XXXX")` `=(x-2+x+2)/(x-6)`

`color(white)("XXXX")` `=(2x)/(x-6)`