Dividing out a variable from a quotient

I don't think I've ever mastered this concept. If I have a problem like , can I just divide the x out to get ?

I know if I look at the first expression like then I could turn x/x into 1, but the expression would look like . The x could get brought back into the quotient if it had a common denominator.

Also, if the sample problem were would that make a difference in mathematical rules for dividing out the x? (As opposed to addition or subtraction).

I hope my question makes sense, if not I can explain more.

Re: Dividing out a variable from a quotient

Quote:

Originally Posted by

**AZach** I don't think I've ever mastered this concept. If I have a problem like

, can I just divide the x out to get

?

No. x is not a factor of the top; you cannot simply cancel out the x.

The correct simplification is , as you did, or alternatively, .