In Japanese,
なくて is a construction that combines ない (in its conjugation form, なく), with the 接続助詞（せつぞくじょし）
て. This results in the same ‘and’ meaning as the standard
て form, but with the negative meaning of ない.
なくて can be translated as ‘to not (A), and…’, or ‘not (A), and…’, depending on what type of word it is used with.
-
お金（かね）がなくて車（くるま）が買（か）えない。
I don't have money, and I can't buy a car.
-
あのケーキは甘（あま）くはなくてまずいです。
That cake is not sweet, and tastes bad. (は is frequently added between the stem form of adjectives and ない. Often, this is just for emphasis)
-
私（わたし）の車（くるま）
は
静（しず）かではなくてガソリンの減（へ）りも早（はや）い。
My car is not quiet, and runs out of gas quickly.
-
あれ
は犬（いぬ）ではなくて猫（ねこ）でもないです。
That is not a dog, and not a cat either.
As discussed in our initial lesson about ない, there are two forms of this particular word. One form is a 助動詞（じょどうし） (auxiliary verb), and is used with verbs. The other form of ない is a 形容詞（けいようし） (
い-Adjective), and is used with nouns,
な-Adjectives, and
い-Adjectives.
The difference between these two, is that the
い-Adjective form may have
は in between it and the word it is connected to (
では in the case of nouns and
な-Adjectives). With verbs, due to ない being a 助動詞（じょどうし）, this is not possible.
-
この風呂（ふろ）は汚（よご）れはなくて、いつもいい匂（によ）いがする。
This bath is not dirty, so it always smells good. (Unnatural Japanese, as は will never come between a verb and ない)
-
この風呂（ふろ）は汚（よご）れなくて、いつもいい匂（によ）いがする。
This bath doesnt get dirty, and it always smells good. (Natural Japanese)
なくて is very similar to
ないで, another structure that is regularly used with verbs (but may not be used with nouns or adjectives).
ないで is far more common when expressing ‘not doing’ something, while
なくて tends to be used almost exclusively for expressing reasons/causes.
-
トーマスにはまだプレゼントをあげないでね。
Please don't give Thomas his present yet. (No particular reason, simply implies ‘without doing’)
-
もらったクッキーを弟（おとうと）にあげなくて、妹（いもうと）にあげた。
I did not give the cookie I got to my brother, but to my sister. (Implies a specific reason for not giving it to the brother)