Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Inequalities
Rational inequalities involve expressions that are ratios of polynomials set in an inequality format. To solve them, one must determine where the rational expression is greater than or less than zero. This often requires finding critical points where the expression is undefined or equals zero, and then testing intervals to establish the solution set.
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Rationalizing Denominators
Interval Notation
Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). For example, the interval (2, 5] includes all numbers greater than 2 and up to 5, including 5 but not 2.
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Critical Points
Critical points are values of the variable where the rational expression is either zero or undefined. These points are essential for determining the intervals to test in the inequality. In the given inequality, finding the critical points involves solving the equations derived from the numerator and denominator, which helps in analyzing the sign of the rational expression across different intervals.
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