[tex]~~~~\sqrt{x +1} = x -1\\\\\implies \left( \sqrt{x+1} \right)^2 = (x-1)^2\\\\\implies x +1 = x^2 -2x +1\\\\\implies x^2 -2x +1 -x-1=0\\\\\implies x^2 -3x = 0\\\\\implies x(x-3) =0\\\\\implies x =0,~ x =3\\\\x = 0~ \text{doesn't satisfy the original equation.}\\\\\text{Hence,} ~x= 3[/tex]
