Solve for ( x ) [ ⁻¹ ( 1-x 1+x )= 1 2 ⁻¹ x, x>0 ]

Step-by-step solution

Given that, ( ⁻¹ ( 1-x 1+x )= 1 2 ⁻¹ x ) Taking L.H.S, we have ( ⁻¹ ( 1-x 1+x ) ) We know that, ( ⁻¹ ( x-y 1+x y )= ⁻¹ x- ⁻¹ y ) So, ( ⁻¹ 1- ⁻¹ x= I 4 - ⁻¹ x ) So, ( 4 - ⁻¹ x= 1 2 ⁻¹ x ) ( I I 4 = 3 2 ⁻¹ x ⁻¹ x= I I 6 ) ( x= 6 x= 1 3 )