AA'XX' and the closely related AA'BB' patterns appear in a number of commonly encountered symmetric 4-proton molecular fragments:
AA'XX' Spectra consist of a maximum of two identical 10-line half spectra, each symmetrical about its midpoint, vA and vX, respectively.
|K| = |JAA' + JXX'|"J" of one ab quartet
|L| = |JAX - JAX'|"d " of both ab quartets
|M| = |JAA' - JXX'|"J" of other ab quartet
|N| = |JAX + JAX'|"doublet"
Each half-spectrum consists of a 1:1 doublet (intensity 50% of the half spectrum) with separation |N|, and two ab quartets, each with "normal" intensity ratios, and apparent couplings (Jab) of |K| and |M| as indicated. Unfortunately, K and M cannot be distinguished, the relative signs of JAA' and JXX' are not known, nor is it known which number obtained is JAA' and which is JXX'. The same ambiguity occurs for JAX and JAX'.
In the situation where JAX = JAX' (i.e. L = 0, A2X2) the spectrum collapses to a triplet. In other words, the effective "chemical shift" of each of the ab quartets is zero, and each gives a single line at A. This is more or less the situation with many compounds of the X-CH2-CH2-Y type, provided that X and Y are not too large, but cause very different chemical shifts.
In the situation where JAA' = JXX' (which is often approximately the case with X-CH2-CH2-Y and p-disubstituted benzenes) the second ab quartet collapses to two lines since M = 0.
To solve an AA'XX" pattern it is necessary to identify the three substructures: "doublet" and the two AB quartets, solve for K, L, M, and N, and then optain the individual couplings.