y=( 1-x^2)/( 1+x^2)= 1-[2x^2/( 1+x^2)]

= 1-2/( 1+x-2){ This is the result of dividing the upper and lower parts of the score by x 2 at the same time}

With X>0, then x-2 is also greater than 0,

Then the range of 2/( 1+x-2) is (0,2).

Then the range of -2/( 1+x-2) is (-2,0).

Therefore, the range of 1-2/( 1+x-2) is (-1, 1), that is, the range of y is (-1. 1).

Where x -2 stands for -2 power of x and x 2 stands for =>, which is a deduction symbol.