The fact that おかげで is N3 grammar is a travesty.

Because it's a really awesome way to thank someone for their help. And saying thank you eloquently makes you look cool in any language.

Dictionary entry:

おかげで
thanks to; owing to; because of

Let's start with a slight variation of this grammar point---a common, polite way to tell your teacher that they are to thank for all kinds of great stuff:

おかげさまで
thanks to you

Example, pls:

A:
東京大学に合格したそうですね。おめでとう。
とうきょう　だいがく　に　ごうかく　した　そうですね。 おめでとう。
I heard that you got accepted to Tokyo University. Congratulations.
Literally: "Tokyo University + に + passing (an exam) + did + heard that (=そうです). + congratulations."
Note: A more literal translation would be, "I heard that you passed the entrance exam for Tokyo University"... since that is how university admissions are handled in Japan--with entrance examinations.

B:
おかげさまで。ありがとうございます。
おかげさまで。　ありがとう　ございます。
I couldn't have done it without you. Thank you.
Literally: "thank to you. + thank you."

Now, I know you must be getting really excited, because Person B just dropped a sentence that is extremely easy to duplicate and is highly useful.

Teacher:
Bro, you're, like, really good at Japanese.

You:
おかげさまで。

But what if we want to "thank" someone or something other than "you?"

Well, then we would need to do this thing I read about in a book: Grammars.

Sentence:

皮膚科でもらった塗り薬のおかげで、にきびがなくなりました。
ひふか　で　もらった　ぬりぐすり　の　おかげで、　にきび　が　なくなりました。
My acne went away thanks to the ointment I got at the dermatologist.
Literally: "dermatology + で + received + ointment + の + thanks to, + pimples / acne + が + went away."

Thanks to A, B.
= A おかげで, B.

Since the word directly before おかげで was a noun, we put a の between them:

塗り薬のおかげで
thanks to ointment

Let's all take a moment to appreciate that the word for "ointment" is:

塗り薬
ぬりぐすり
ointment
Literally: "paint-medicine"

Well, another literal translation might be something like "plaster-medicine" or "smear-medicine." Personally, though, I'm on team "paint-medicine."

Speaking of which, when I googled "paint medicine" (for, you know, research purposes), this majestic beast popped up on my laptop screen:

And I learned a new term: "medicine hat horse."

Could today get any better?

\(*o*)/

Sorry, what was I talking about?

Oh yeah, ointment!

Err, I mean, grammar...

母が背中を押してくれたおかげで、起業する決心がつきました。
はは　が　せなか　を　おして　くれた　おかげ　で、　きぎょう　する　けっしん　が　つきました。
It was thanks to a supportive push from my mom that I got the resolve to start my own business.
Literally: "mother + が + back + を + push (and) + gave (me) + thanks to, + starting a business + do + determination / resolution + が + stuck."

This time we had a past tense plain form verb right before おかげで.

Since おかげで gets real personal with plain-form verbs, we can put them right next to each other:

押してくれたおかげで
thanks to being pushed

What if you're not 100% sure that A is to thank for B?

Well...

To express our doubt, we can swap out で with か：

タバコをやめたおかげか、最近ご飯がおいしく感じるようになった。
タバコ　を　やめた　おかげか、　さいきん　ごはん　が　おいしく　かんじる　ように　なった。
Lately food has been tasting better, maybe thanks to the fact that I quit smoking.
Literally: "tobacco + を + quit + thanks to? + lately + food + が + tastily + feel + ように + became."

We also don't use で when おかげ is at the very end of our sentence.

In that case, で (which tends to only come at the end of sentences that are requests/commands) becomes です：

わたしが無事に卒業できたのは、熱心に勉強を手伝ってくれた友人たちのおかげです。
わたし　が　ぶじ　に　そつぎょう　できた　の　は、　ねっしん　に　べんきょう　を　てつだって　くれた　ゆうじん　たち　の　おかげ　です。
I was able to graduate without problems thanks to my friends, who enthusiastically helped me with my studies.
Literally: "I + が + safely / without problems + graduation + was able to do + のは, + enthusiastically + studies + を + help (and) + gave (me) + close friends + の + thanks to."

That's all for this one.

I would tell you to go study, but I have a feeling you're faced with more pressing matters at the moment--like googling different breeds of horses.