Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. (x + 1)/(x - 5) > 0

Rational inequalities involve expressions that are ratios of polynomials set in relation to an inequality (e.g., >, <). To solve them, one must determine where the rational expression is positive or negative, which often requires finding critical points where the numerator or denominator equals zero.

Critical points are values of the variable that make the numerator or denominator of a rational expression zero. These points divide the number line into intervals, which can be tested to determine where the inequality holds true. For the inequality (x + 1)/(x - 5) > 0, the critical points are x = -1 and x = 5.

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). For example, the solution set for the inequality can be expressed in interval notation to clearly show the values of x that satisfy the inequality.