Can I go from UFCF to LFCF? Help a monkey understand, please

Hi, I have an interview coming up and had a question about UFCF and LFCF.

According to my textbook:

1) FCF = Cash flow to creditors + Cash flow to stockholders

     FCF = Operating cash flow - Net Capital Spending - Changes in net working capital

     where:

     UFCF* = EBIT - Taxes + D&A - CapEx - Changes in NWC

2) Cash flow to creditors = Interest paid - Net new borrowing

3) Cash flow to stockholders = Dividends paid - Net new equity raised

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I know that LFCF is only available to equity investors. The formula I came across is:

LFCF = Net Income + D&A - CAPEX - Changes in NWC

So, my question is:

A) Is the "cash flow to stockholders" in my textbook equivalent to LFCF? Initially, it seemed to me like it was just the portion of the FCFF that was available to stockholders. When I tried using the LFCF formula above on the numbers from my textbook, I got:

          LFCF > Cash flow to stockholders

I am assuming this is because, with the UFCF formula, I am starting with the premise that the FCF I am calculating will be available to everybody (i.e. interest is not subtracted). On the other hand, the LFCF assumes that the FCF I am calculating will exclusively be available to stockholders (i.e. interest is already subtracted by using NI).

Otherwise, the following would be true: LFCF = UFCF - Cash flow to creditors

Could someone explain where I am wrong? I doubt I am making any math errors. I want to understand the difference between UFCF and LFCF conceptually. Why can't I simply take UFCF and subtract the portion available to creditors to get LFCF? Are any of my formulas wrong?

Thank you very much in advance!

Edit: I tried again to calculate LFCF with my textbook numbers. This time, I added net new borrowings (the amount by which long-term debt increased). So, I did this:

     LFCF = Net Income + D&A - CAPEX - Changes in NWC + Net new borrowings

     Thus, LFCF = Cash flow to stockholders = UFCF - Cash flow to creditors

But, I still am not understanding why adding net new borrowings made that difference? Was my original LFCF wrong? Shouldn't I be trying to eliminate debt payments and interest when calculating LFCF? Thank you again, and I apologize for the long post. I hope my questions are not confusing.