Solution:

Given: output of the system $y(n)=x(n)+\frac{1}{x(n-1)}$

For $\mathrm{n}=-1 ; \quad y(-1)=x(-1)+\frac{1}{x(-2)}$

For $\mathrm{n}=0 ; \quad y(0)=x(0)+\frac{1}{x(-1)}$

For $\mathrm{n}=1 ; \quad y(1)=x(1)+\frac{1}{x(0)}$

For all values of ‘n’, the output depends on present and past inputs. Therefore, the system is causal.