Answer
$\frac{4}{x}$
Work Step by Step
$(1+\displaystyle \frac{1}{x})^{2}-(1-\frac{1}{x})^{2}=[(1+\frac{1}{x})-(1-\frac{1}{x})][(1+\frac{1}{x})+(1-\frac{1}{x})]
=(1+\frac{1}{x}-1+\frac{1}{x})(1+\frac{1}{x}+1-\frac{1}{x})=(\frac{2}{x})(2)=\frac{4}{x}$
