Average Values. Consider the function

$f(x)=\frac{1}{x^{2}1}$

Desmos

Let $a$ be an integer greater than $)=(2,3,4,$dots Find an algebraic relationship between $A,$ the average value of $f(x)$ on the interval $\frac{1}{n},1$ and $A,$ the average value of $f(x)$ on the interval $1,n.$ Hint: Calculate these averages for some small values of $n$ and look for a pattern or formula. State your answer as an algebraic relationship between $A_2$ and $A_2.$

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