Let f (x-1 / x) = the square of X divided by the fourth power of 1 + X

Let f (x-1 / x) = the square of X divided by the fourth power of 1 + X

The sign ^ is used to denote the power operation
Transform the right end of the equation. Divide the numerator and denominator by x ^ 2 at the same time
Let the numerator be 1 and the denominator be x ^ 2 + 1 / x ^ 2. And x ^ 2 + 1 / x ^ 2 = (x - 1 / x) ^ 2 + 2
In this way, X - 1 / X is exactly the same as the expression in the left bracket of the equation in the title
The specific process is as follows
x^2/(1+x^4)
=1/(1/x^2 + x^2)
=1/[(x- 1/x)^2 +2)
=f(x -1/x)
therefore
f(x) = 1/(x^2 + 2)