The equation of curve passing through $\left(2, \frac{7}{2}\right)$ and having slope $1-\frac{1}{x^2}$ at (x, y) is :

$y=x^2+x+1$ $x y=x+1$ $x y=x^2+x+1$ $x y=y+1$

$x y=x^2+x+1$

$\frac{d y}{d x}=1-\frac{1}{x^2} \Rightarrow y=x+\frac{1}{x}+c$ At $(2,7 / 2) \frac{7}{2}=2+\frac{1}{2}+c \Rightarrow c=1$ Therefore $y=x+\frac{1}{x}+1 \Rightarrow xy=x^2+x+1$ Hence (3) is the correct answer.