Find the maximum according to a parameter

I'm new to Mathematica. I want to find the maximum of the functions:

Find maximum[(1 + y)^2/((1 + y)^2 + (1 + x)^2)* 5 - y - (1/((1 + x)^2 + 1))*5 && 0 < y < 2 , y]

So I want to find the maximum of the previous function, with and in the range of 0 to 2, taking x as a parameter. However he showed the error.

FindMaximum :: nrnum: The value of function 1. + (5 (1 + x) ^ 2) / (1+ (1 + x) ^ 2) - (5 (2. + x) ^ 2) / (1+ (2. + x) ^ 2) is not a real number in {y} = {1.}

How can i fix this? It only works if I enter a certain value for x (such as x = 1).

Thank you very much to all!