Given: QUANTITY A: \(\frac{(xy)^2 - x^2}{(x+1)(y^2 - 1)}\)

Apply the power of a product law to quantity A's numerator:
QUANTITY A: \(\frac{x^2y^2 - x^2}{(x+1)(y^2 - 1)}\)

Factor the numerator:
QUANTITY A: \(\frac{x^2(y^2 - 1)}{(x+1)(y^2 - 1)}\)

Since we're told \(y \neq \pm1\), we can be certain that: \(y^2 - 1\) does not equal 0, which means we can safely divide numerator and denominator by \(y^2 - 1\) to get:
QUANTITY A: \(\frac{x^2}{x+1}\)

At this point we can see the two quantities are equal.

Answer: C