What characteristic does the square of the denominator have in a rational inequality?

In the context of rational inequalities, when dealing with a rational expression that has a denominator, the square of the denominator plays a significant role in the evaluation of the inequality.

The primary characteristic of a squared number is that it is always non-negative, meaning it cannot be negative. Since the denominator is a real number, when we square it, regardless of whether the original denominator is positive or negative, the result is always a non-negative value. This attribute is crucial when analyzing the behavior of the rational expression, especially in determining the intervals where the inequality holds true.

Additionally, squaring any real number, including the denominator of a fraction, leads to a positive result unless the denominator itself is zero (which would make the rational expression undefined). However, when we focus strictly on the behavior of the square itself, we can conclusively state that it results in a positive quantity whenever the denominator is not zero.

Therefore, in a rational inequality, the square of the denominator will always be positive when defined, underscoring the correct answer to be that it will always be positive.