First recognize the numerator as a difference of squares: a^2 - b^2 = (a - b)(a + b). After factoring, one factor is common with the denominator, so it can be cancelled. Use difference of squares: x^2 - 1 = (x - 1)(x + 1), then cancel x - 1. The restriction given in the question only prevents division by zero. The simplified answer is x + 1.