Take bus 420 just outside Maastricht central station and it takes you directly to Aachen central station. It costs 4,53 euro one way (buy a 'strippenkaart' at the trainstation in Maastricht or in the bus).
Or take a train direction Heerlen (platform 2), change trains at Heerlen (platform 1) to go to Aachen.
That takes an hour too. The price is 4,30 euro.
Information about 'strippenkaart' (strip ticket) at Netherlands Transportation Tips by ATLC (scroll down to 4th tip)
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