The equation x+1−x−1=4x−1

Squaring on both sides, we get(x+1)+(x−1)−2x2−1=4x−1⇒ 2x−2x2−1=4x−1⇒ 1−2x=2x2−1Again squaring on both sides, 1+4x2−4x=4x2−4⇒  4x=5  ⇒  x=54 .∴  only one solution is possible