Debt to Assets is (total debt)/(total assets)
the book claims that Debt to Capital is (total debt)/(total debt + equity)
Since Equity = total assets - total debt, aren’t these two equations identical?
Debt is not the same as liabilities. Debt means liabilities that bear interest: bonds payable, and lease liabilities, for example. But there are other liabilities – accounts payable, wages payable, deferred tax liabilities, and so on – that do not bear interest; they’re not debt. Thus, while it’s true that
Equity = Total assets – Total liabilities,
in general,
Equity ≠ Total assets – Total debt.
It is true that
Equity ≤ Total assets – Total debt,
and, usually,
Equity < Total assets – Total debt.
Is the issue with the definition of what is actually Debt.
Asset = Liabilities + Equity ----------(1)
Debt-to-Asst = Total Debts/Total Assets ------------(2)
It has also been mentioned in Schweser’s Notes that different analysts compute firm’s debt differently. Some only take into account interest-bearing liabilities whereas other consider current liabilities (such as account payables,trade payables) as a source of funding for the firm.
In the former case, (1) can be rewritten as:
Total Assets = Liabilities not classified as debt + ( Liabilities classified as debt + Equity )
Total Assets = Liabilities not classified as debt + Total Capital
In the latter case, (1) will be rewritten as:
Total Assets = Debts + Equity = Total Capital , since definition of debt is expanded to include current liabilities of the firm.
In either case, equation (2) will be different since the definition of debt is different in each case.
There is a similar thread on this posted by other regarding one of the questions in SN/CFAI EOC.
Hope this helps a bit 
Cheers,
Ernest
yeah, S2000magician summarise it nicely.
Thanks, Ernest.
I see your comment that debts are not the same thing as liabilities
In the textbook, an example states that “debt to asset” ratio is 60%. It then asks us to find ROE, by first calculating leverage ratio a.k.a. Assets/Equity
Isn’t this impossible since debt =/= liability, and therefore we cannot calculate equity without seeing a balance sheet?
In general, yes.
In practice (i.e., on the Level I CFA exam), they may fudge and use debt and liabilities interchangeably. If they ask you about debt and don’t break down liabilities, assume that debt = liabilities. It’s stupid, but it’s the best you can do under the circumstances.