Rational Inequalities
We adapt the preceding method when an inequality involves rational expressions.
We call these rational inequalities.
To solve a rational inequality:
a. Change the inequality symbol to an equals sign and solve the
related equation.
b. Find the numbers for which any rational expression in the
inequality is not defined.
c. Use the numbers found in steps (a) and (b) to divide the number
line into intervals.
d. Substitute a number from each interval into the inequality. If the
number is a solution, then the interval to which it belongs is part
of the solution set.
e. Select the intervals for which the inequality is satisfied and write
set-builder or interval notation for the solution set.