If u=x y^2 ⁻¹ ( y x ) , then x u x +y u y is equal to

Step-by-step solution

Given that, aligned & u=x y^2 ⁻¹ ( y x ) & u x =y^2 ⁻¹ ( y x )+x y^2 1 1+ y^2 x^2 (- y x^2 ) &=y^2 ⁻¹ ( y x )- x y^3 x^2+y^2 & u y =2 x y ⁻¹ ( y x )+x y^2 1 1+ y^2 x^2 ( 1 x ) &=2 x y ⁻¹ ( y x )+ x^2 y^2 x^2+y^2 & x u x + y u y =x y^2 ⁻¹ ( y x )- x^2 y^3 x^2+y^2 & x u x +y u y =3 x y^2 ⁻¹ y x =3 u aligned