How would I evaluate the following fraction and express it properly?
Should I multiply and take the reciprocal of the bottom or would the brackets block me from taking the reciprocal?
Well, what you can do is write it like this:
which is what the initial expression means.
Then by the rule "to divide by a fraction you turn it upside down and multiply instead" you then get:
hence the answer.
Alternatively you can take the original expression:
... and multiply top and bottom by the reciprocal of what's on the bottom:
... which is probably the clearest way to explain what's going on.