The value of ⁻¹ ( x y )- ⁻¹ ( x-y x+y ) (where, x, y>0 ) is

Step-by-step solution

⁻¹ ( x y )- ⁻¹ ( x-y x+y ), ( x, y>0) = ⁻¹ x y - ( x-y x+y ) 1+ x(x-y) y(x+y) aligned & [ ⁻¹ A- ⁻¹ B= ⁻¹ A-B 1+A B ] =& ⁻¹ ( x²+x y-x y+y² x y+y²+x²-x y ) =& ⁻¹ ( x²+y² x²+y² ) =& ⁻¹(1)= ⁻¹ ( 4 )= 4 aligned