You can put this solution on YOUR website!
The last thing we want to do is start multiplying right away. Perhaps ironically what we want to do is "un-multiply", i.e. factor first!
I'm going to do them separately. The first numerator:
This will factor by grouping. Group:
Factor the GCF from each group. (This point in factoring by grouping is one of the rare times we actually factor out a GCF of 1!)
If we're lucky the "non-GCF" factors match. Our "non-GCF" factors, the (a+b)'s, match. So we can factor them out:
The first denominator:
Factor the GCF:
I'm even going to factor the 4 into primes:
The second numerator.
This is already pretty much factored. But I will factor the 6 into primes:
The second denominator:
First the GCF:
Then a difference of squares pattern:
Replacing the numerators and denominators with the factored forms:
The reasons we factored are:
When reducing fractions, only factors may be canceled!! So we need to see the factors to know if anything will cancel.
When multiplying fractions you are allowed to cancel a factor in one fraction's numerator with a factor in another fraction's denominator. Multiplying fractions is the only time this is allowed. Not only is it allowed but it is an extremely good thing to do before you multiply. It makes the rest of the problem much easier!
Looking at the factored fractions we can see a lot of factors to cancel:
leaving:
Obviously this is much, much easier to multiply than what we started with. And, if we have truly factored everything fully, then the fraction we end up will not reduce. Multiplying we get:
which simplifies to:
(