Clarification on the Quotient Rule

Hello, and thanks for your help in advance.

I recently learned the quotient rule in finding the derivative of more complicated expressions and had a question on it.

The way we've been taught is that when given f(x)/g(x), the derivative is [g(x)*f'(x)-f(x)*g'(x)]/g(x)^2

My question has to do with when the more complicated expression is in the denominator of the function we are to differentiate. A good example is stated below:

__ ....x..... __

(x+2)^2

(The periods are present just to make the fraction look better.)

In this situation, the denominator of the derivative gets very complicated if I square [(x+2)^2], so is it legitimate to switch which expression is f(x) and g(x), making the derivative have x^2 in the denominator and changing the numerator accordingly?

I realize my question is a bit confusing, so please don't hesitate to ask questions...just hoping to keep expressions as simplified as possible.