We form a “but” in Japanese by appending the が particle to the end of the clause.

旅行りょこうきたいですやすみがれません。
I want to go on holiday but I can’t take time off.
普段ふだん自炊じすいします今日きょう外食がいしょくしたいです。
Normally I cook myself, but today I want to eat out.
試験しけん勉強べんきょう大変たいへんです頑張がんばってください。
It’s tough studying for exams, but please do your best.
部屋へやひろくないです家賃やちんたかいです。
My room is not big, but the rent is expensive.

Grammatically speaking, が can also be used with standard form of the verbs but you only ever see this in formal writing (e.g. newspapers). The below was an actual headline from Newsweek.

イラン人がくるしむ水不足みずぶそくだが中東ちゅうとう対立解消たいりつかいしょうへのチャンスにできる
Iranians suffering from water shortages, but it could be a chance to resolve the conflict in the Middle East.

In conversation the particle けど is typically used instead.

さけめるけど普段ふだんはあまりまない。
I can drink alcohol but don’t do so that often.

Note: あまり is used with the negative to mean “not so much” or “not too often” etc.

あまり勉強べんきょうしなかったけど、なんとなく試験しけん合格ごうかくしたよ。
I didn’t really study, but somehow I managed to pass.
みせふくやすけどしつくない。
The stores clothes are cheap, but the quality isn’t good.

Note that the topic particle is used in the first clause in the last example. You may think we need to use が because we are connecting the noun (clothing) with the adjective “cheap” but then the topic of the sentence would be ambiguous (and would have readers wondering, “The quality of what is good?”

その番組ばんぐみ面白おもしろけど仕事しごといそがしくて時間じかんがない。
That TV programme is funny, but I’m busy with work and don’t have time to watch it.
新幹線しんかんせん便利べんりけど、おかねがかかる。
The bullet train is convenient, but it’s expensive.
納豆なっとうきらいじゃないけど、めったにべない。
I don’t hate natto, but very rarely eat it.

Note: めった is used with the negative to express that you don’t do something very often. It has more emphasis than あまり.

けど can also be used in polite conversation, but you would not see it in written text (unless on maybe someone’s personal blog).

あのひと会計士かいけいしですけど数学すうがく得意とくいではありません。
That person is an accountant, but he’s not good at maths.

In fact there are three other variations of けど: けれど, けども, and けれども. The nuance is broadly the same for all four and grammatical usage is identical. けど is by far the most commonly used.

成績せいせきわるくないけれど、もうすこ頑張がんばれる。
My grades aren’t bad, but I could try a little harder.
成績せいせきわるくないけども、もうすこ頑張がんばれる。
My grades aren’t bad, but I could try a little harder.
成績せいせきわるくないけれども、もうすこ頑張がんばれる。
My grades aren’t bad, but I could try a little harder.
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