(y/x)'/[ 1+(y/x)？ ]=? (x？ +y？ )'/(x？ +y？ )

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

Y is a function of x, and the derivative should use the derivative rule of compound function.

(y' x-y)/(x？ +y？ )=(x+y y')/(x？ +y？ )?

y' x-y=x+y y'→y'(x-y)=x+y

y'=(x+y)/(x-y)