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In one of the grammar questions for N3, I saw one for which I couldn't
understand the reason why のでは is used.

> この英会話講師のアルバイトに応募したきっかけは、先輩からの紹介です。私の専門は言語学ですので、その知識が生かせる「
> 」、と思い、応募いたしました。文法に詳しいので、英語はもちろん、日本語での文法の説明もできます。

Possible answers are

> 1) から ２）とか ３）なんて ４）のでは

The answer marked as correct is のでは. However, I don't understand why. I know
that のでは is used in sentences like のではない。However, that's not he case here.
Also as ので、when implying reason. However in that case I don't see は added.
When searching through google I found more cases where you can use like this
"一歩間違えば指先に刺さるのではと思ってしまう".

However, I don't understand which grammar rule allows for this usage of のでは。
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2015-11-09T18:21:29.853
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grammar usage jlpt ellipsis
Question about usage of 「のでは」
The "のでは" here implies it's one's (humble) opinion or suspicion.

One can also say "その知識が生かせるかと思い".

I presume this usage is related to "のではない".
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2015-11-10T01:20:35.653
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You are close. The omitted phrase is その知識が生かせるのではない **か** , where か is the
question marking particle you must know well.

It says "Can't I make use of the knowledge? (I can!)" rather than saying "I
can't make use of the knowledge".

Similarly, 刺さるのでは in that context means 刺さるのでは **ない（だろう）か** , meaning "I
wonder if it pricks".
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2015-11-10T11:16:19.410
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2015-11-10T11:46:06.320
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**のでは describes possibility.**  

> 私の専門は言語学ですので、その知識が生かせる「 」、と思い、応募いたしました。

I applied this opportunity because my proficient is Linguistics.  
It's possible to take advantage of my knowledge.  

Japan's Cultural expression way, we do not insist directly.  
If this is English,  
I am sure that I can take advantage of my skills in this field.  
In Japan, we softly insist , that's why のでは is added.  
のでは have effect to make the things more softly.

> 私の専門は言語学ですので、その知識が生かせると思い、応募いたしました。  
>

In gramatical,  
This sentence is also collect ,perfectly works.  
You can use when you want to approach strongly.
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