To solve the inequality, we can start by expanding the expression on the left side:

(x+1)(x-1) = x(x-1) + 1(x-1) = x^2 - x + x - 1 = x^2 - 1

Now, we have the inequality:

x^2 - 1 < 0

To solve this inequality, we can factor the expression:

(x-1)(x+1) < 0

Now, we can analyze the sign of each factor:

When x < -1, both factors (x-1) and (x+1) are negative, so their product is positive.

When -1 < x < 1, the factor (x-1) is negative and the factor (x+1) is positive, so their product is negative.

When x > 1, both factors (x-1) and (x+1) are positive, so their product is positive.

Therefore, the solution to the inequality is:

-1 < x < 1