a) Why are you trying so hard?
b) Why you're trying so hard?
Is you're (b) an acceptable contraction form of are you (a) when I want to keep the sentence in a question form?
Is there another way to contract (this) question in English?
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One can indeed use a contraction in question:
Why don't you do it today?
But "you're" is a contraction of "you are" not of "are you " so it does not work in sentence b) from the question, which expands to:
Why you are trying so hard?
which is not really grammatical, and certainly does not carry the same meaning as sentence a).
"you're" can be used in a question in any case that "you are" can be. For example:
You're not going to leave early, are you?
you're is generally a contraction of "you are", so saying "why you are trying so hard?" would not sound totally correct in this instance. In general though there's no particular reason to not use a contraction in a question.
However, if formulated slightly differently it would sound idiomatic. Consider "You have to ask yourself why you're trying so hard".