If x 1+y +y 1+x =0 , then d y d x is equal to

Step-by-step solution

Given that or x 1+y =-y 1+x On squaring both sides, we get array cc & x^2(1+y)=y^2(1+x) & x^2-y^2+x^2 y-x y^2=0 & (x-y)(x+y)+x y(x-y)=0 & (x-y)(x+y+x y)=0 array x-y 0 because it does not satisfy the Eq. (i) aligned & x+y+x y=0 & y=- x 1+x & aligned On differentiating w.r.t. x , we get aligned d y d x & =- (1+x)(1)-x(1) (1+x)^2 & =- 1 (1+x)^2 aligned