Trying to update date range every month

We have a spreadsheet I'm creating for a recon that we can just input the new date every month (last day of each month) and end up with a description for the journal entries that says "Company mm/dd - mm/dd/yy." I can create this with the usual text strings, but I want to use an IF statement for months that end in 30 vs 31.

If there's an easier way to pull the first and last of the month of the date that's entered, let me know as well.

Currently, I have ="NASDAQ"&" "&TEXT(A3-29,"mm/dd")&" "&"- "&TEXT(A3,"mm/dd/yy") which can pull NASDAQ 11/01 - 11/30/17. A3 is the date entered as 11/30/2017, for example.

How would I be able to work in an IF statement that basically says if dd = 30, subtract 29 from A3 and dd = 30, subtract 30 from A3?

This mess below is what I have right now, which of course Excel says is a hot mess.

IF(A3=Day(30)["NASDAQ"&" "&TEXT(A3-29,"mm/dd")&" "&"- "&TEXT(A3,"mm/dd/yy")],["NASDAQ"&" "&TEXT(A3-30,"mm/dd")&" "&"- "&TEXT(A3,"mm/dd/yy")]

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