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x+2017x=⌊x⌋+2017⌊x⌋x + \dfrac {2017}{x} = \lfloor x \rfloor + \dfrac {2017}{\lfloor x \rfloor}x+x2017=⌊x⌋+⌊x⌋2017 If the sum of all non-integer real solutions xxx to the above expression can be represented as ab\frac{a}{b}ba, where aaa and bbb are coprime integers and bbb is positive, find a+ba+ba+b.
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