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れる

Saying you can: the potential form

食(た)たべられる, 話(はな)はなせる, できる — ability and possibility.
要点The idea
The potential form says you can do something: る-verbs drop る and add られる, and う-verbs change to the e-sound and add る.
DictionaryCan doMeaning
食(た)たべるtaberu食(た)たべられるtaberarerucan eat
見(み)みるmiru見(み)みられるmirarerucan watch, get to see
飲(の)のむnomu飲(の)のめるnomerucan drink
話(はな)はなすhanasu話(はな)はなせるhanaserucan speak
行(い)いくiku行(い)いけるikerucan go
買(か)かうkau買(か)かえるkaerucan buy
するsuruできるdekirucan do
来(く)くるkuru来(こ)こられるkorarerucan come
食(た)たべられる and 見(み)みられる are also the passive, a later topic; context tells them apart.
日本語(にほんご)にほんご が 話(はな)はなせます。nihongo ga hanasemasu.I can speak Japanese.The thing you can do usually takes が (を is also heard).
納豆(なっとう)なっとう が 食(た)たべられない。nattou ga taberarenai.I can't eat natto.
明日(あした)あした 来(こ)こられる?ashita korareru?Can you come tomorrow?
A一人(ひとり)ひとり で 行(い)いく。hitori de iku.I'll go alone.
B一人(ひとり)ひとり で 行(い)いける。hitori de ikeru.I can go alone.
Only the ending changes: く → ける, and doing becomes being able to do.

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