The equation of curve passing through \( \left(2, \frac{7}{2}\right...

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The equation of curve passing through \( \left(2, \frac{7}{2}\right) \) and having slope \( 1-\frac{1}{x^{2}} \) at \( (x, y) \)
\( \mathrm{P} \) is :
(A) \( y=x^{2}+x+1 \)
(B) \( x y=x+1 \)
(C) \( x y=x^{2}+x+1 \)
(D) \( x y=y+1 \)
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