I am writing a formal school paper (by formal I mean, with an abstract, a bibliography and $20$ pages in length) on mathematics (it is called "Extended Essay", for those having knowledge of the International Baccalaureate) and I was wondering whether I should include algebra steps as in $\frac{(2k+1)^{-2}}{1-(2k+1)^{-2}} = \frac {1}{4k(k+1)}.$ In fact I can do this in my head and I am sure that the external examiner will not have the slightest problem understanding steps. However, I only fear that when you don't show any steps it is as if you copied it from a book or so, which is not case.
In general for academic papers (like important undergraduate mathematical projects), should I include such steps or other non-algebraic steps that are sort of obvious and that the reader can pretty much understand even by grabbing pen and paper in the worst case?
Thanks in advance.