Solve each rational inequality. Give the solution set in interval notation. (9x-8)/(4x^2+25)<0

Key Concepts

Rational Inequalities

Rational inequalities involve expressions where one polynomial is divided by another, and the inequality compares this fraction to zero. To solve these inequalities, we need to determine where the rational expression is positive or negative, which often involves finding critical points where the numerator or denominator equals zero.

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 intervals) or excluded (open intervals). Understanding how to express solution sets in interval notation is crucial for clearly communicating the results of inequalities.

Sign Analysis

Sign analysis is a method used to determine the sign (positive or negative) of a rational expression across different intervals. By testing values from intervals defined by the critical points, we can identify where the expression satisfies the inequality. This process is essential for accurately finding the solution set of the inequality.