As you probably know, dividing by a fraction is done by multiplying by its reciprocal. So this is where we'll start:
We now have a product of fractions. I hope you know that when you multiply fractions it is OK to cancel common factors, if any, before you multiply. In fact it is more than just OK. It is usually a good idea to do this because then
the multiplication is easier with reduced fractions
Reducing the fraction after the multiplication is easier.
Both of these are going to be especially true with this problem. After all, would you really want to multiply all this out, add like terms and then factor out the result?? So we will cancel common factors first. And to have common factors we need to factor:
(This is one of the ways we use factoring. It pays to get good at it.) Now we can cancel the factors that are common to the numerators and the denominators. (Remember when we are multiplying fractions (and only multiplying, not adding subtracting or dividing (before it's turned into a multiplication) we can cancel across fractions.)
leaving us with:
which simplifies to:
which will not reduce any further. (Note how easy these last steps were after we canceled factors!
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