Number of real solutions of the equation x−1x+1−1x=x is

We have x−1x+1−1x=x---1⇒x−1x−1−1xx−1x−1−1x=x⇒ x−1x−1+1xx−1x−1−1x=x⇒ x−1x=x−1x−1−1x----2Adding (1) and (2), we get1−1x+x=2x−1x⇒ x−1x−2x−1x+1=0⇒ x−1x2-21x−1x+12=0 ⇒ x−1x−12=0⇒x−1x=1⇒ x2−x−1=0⇒ x=1±52 As x=1−52 does not satisfy the given equation.