UKMT Intermediate Mathematical Challenge, 2020

For any fixed value of $x$, which of the following four expressions has the largest value? $(x+1)(x-1)$, $(x+\frac{1}{2})(x-\frac{1}{2})$, $(x+\frac{1}{3})(x-\frac{1}{3})$, $(x+\frac{1}{4})(x-\frac{1}{4})$

(A) $(x+1)(x-1)$ (B) $(x+\frac{1}{2})(x-\frac{1}{2})$ (C) $(x+\frac{1}{3})(x-\frac{1}{3})$ (D) $(x+\frac{1}{4})(x-\frac{1}{4})$ (E) it depends on the value of $x$