(x+2):(x^2+6)

[nameVoid]

I have a worksheet with problems containing a : between terms on some problems ..

(x+2):(x^2+6) what does this mean

[Dunkle]

\frac{x+2}{x^2+6} perhaps?

[whybother]

: usually means "such that", ie. x : x < 2, "x, such that, x is less than 2". Obviously, this doesn't apply here...

: also is used to denote field extensions... but that's clearly even less likely.

I'd ask your teacher. It could be division, but they could also be defining some special operation for you to practice.