Solve the rational inequality. Write the answer in interval...

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Key Concepts

Domain Restrictions

Domain restrictions are the values that make the denominator of a rational expression zero, rendering the expression undefined. Such restrictions must be excluded from the solution set when solving rational inequalities.

Interval Notation

Interval notation is a compact way to represent subsets of real numbers. It is used to denote the set of solutions to an inequality by specifying the endpoints of the intervals along with whether each endpoint is included or excluded.

Rational Inequalities

Rational inequalities involve expressions formed as a ratio of two polynomials. To solve them, one typically determines where the expression equals zero or is undefined, then analyzes the expression’s sign on the intervals created by these critical points.

Critical Points

Critical points are the values where either the numerator or the denominator is zero. These points divide the number line into intervals and are crucial in determining where the inequality holds, as they signal potential sign changes and domain restrictions.

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