What is the procedure for handling a rational inequality in the form of a fraction?

When dealing with a rational inequality represented as a fraction, the key aspect is to ensure that the manipulation of the inequality maintains its validity. To do this correctly, one effective approach involves multiplying by the square of the denominator.

The reasoning behind this choice is that squaring the denominator ensures that the result remains positive, regardless of the value of the original denominator. This serves a dual purpose: it eliminates the fraction and also prevents any change in the direction of the inequality, which can occur if the denominator is negative. By squaring the denominator, the transformation preserves the equality's nature, allowing for a correct analysis of the inequality once the rational component is removed.

This method allows us to focus on the resulting polynomial inequality without the complications of the threshold values introduced by the denominator. Thus, making the task simpler and ensuring the solution remains valid across the domain being considered.