〜おかげで
thanks to (a good result)
Noun + のおかげで · Plain form + おかげで (な-adj + な)
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おかげで gives the cause of something good, with a note of gratitude: 先生のおかげで合格できました, "thanks to my teacher, I passed". After a noun it takes の; after a verb or adjective it follows the plain form directly: 薬を飲んだおかげで, 天気がよかったおかげで.
Its opposite is せいで, which blames the cause for something bad. Picking the wrong one changes the whole feeling of the sentence.
おかげさまで is a set phrase for answering "how are you?" or "how did it go?": はい、おかげさまで, "fine, thank you". It thanks the other person politely, even if they didn't do anything in particular.
Used for a bad result, おかげで turns sarcastic: 君のおかげで遅刻したよ, "thanks a lot, you made me late".
Examples
先生のおかげで、試験に合格できました。
Thanks to my teacher, I was able to pass the exam.
薬を飲んだおかげで、熱が下がった。
Thanks to the medicine, my fever went down.
友達が手伝ってくれたおかげで、早く終わりました。
Because my friend helped me, I finished early.
天気がよかったおかげで、楽しい旅行になりました。
Thanks to the good weather, it turned into a fun trip.
「お元気ですか。」「はい、おかげさまで。」
"How are you?" "Fine, thank you."