A rational inequality is an inequality that involves a rational expression, which is a ratio of two polynomials. Solving a rational inequality typically involves finding the critical points where the expression is undefined or equals zero, and testing intervals to determine where the inequality holds true.

Rational Inequality

A rational expression is a fraction where both the numerator and the denominator are polynomials, and it is defined for all values except where the denominator is zero. Simplifying rational expressions involves factoring polynomials and canceling common factors to reduce the expression to its simplest form.

Rational Expression

Ratio of two polynomials

Solving a rational inequality

Critical points of a function are values in the domain where the derivative is zero or undefined, often corresponding to local maxima, minima, or points of inflection. Analyzing these points helps in understanding the behavior and shape of the graph of the function, crucial for optimization and problem-solving in calculus.

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