Is this a valid way to simplify complex fractions?

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    Complex Fractions
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The discussion centers on simplifying the complex fraction [(3 - (3 + h))/(3(3+h))]/h. The original poster questions the validity of the simplification steps provided in their book. They initially attempt to multiply the numerator by the inverse of the denominator, leading to confusion in the simplification process. Ultimately, they realize their mistake in equating different forms of the expression. The key takeaway is the importance of correctly handling fractions and recognizing that different algebraic manipulations can yield different results.
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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
 
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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
 

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