Is this a valid way to simplify complex fractions?

[bobsmith76]

step 1. [(3 - (3 + h))/(3(3+h))]/h

step 2. -h/(3(3+h)h

My book says that those steps are valid. I don't see how.

If you want my opinion, I times the numerator (3 - (3 + h))/(3(3+h)) by the inverse of the denominator h/1 which makes:

step 2. -h/(9+3h) * h

step 3. -h/(9+3)

step 4. -h/12

 

[bobsmith76]

Never mind. I figured out what I was doing wrong.

In a simpler format

(a/(2 + 3a)) * a

where a = 3

is not the same as

a/2 + 3