Another JEE Mains problem

Algebra Level 5

f(x)=1{x+1}x2+2x\large {f(x)=\frac{1}{\sqrt{\{x+1\}-x^{2}+2x}}}

If the domain of f(x)f(x) above, where {x+1}\{x+1\} denotes the fractional part of x+1x+1, can be expressed as (abc,c)\{d}\left(\dfrac{a-\sqrt{b}}{c},c \right)\backslash \{d\}, where aa, bb, cc, and dd are coprime integers and \{d}\backslash \{d\} denotes excluding the value dd, find a+b+c+da+b+c+d.

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