Rational Inequalities
To solve a rational inequality, create a sign graph just as you did for higher order inequalities. This time, you'll have to remember to check for extraneous solutions because the denominator cannot equal \(0\).
Example 1: Solve the inequality: \(\Large{\frac{x-1}{x}+\frac{x-3}{x+1}\ge\frac{3x^2-4x-3}{x^2+x}}\).
To solve a rational inequality, create a sign graph just as you did for higher order inequalities. This time, you'll have to remember to check for extraneous solutions because the denominator cannot equal \(0\).
Example 1: Solve the inequality: \(\Large{\frac{x-1}{x}+\frac{x-3}{x+1}\ge\frac{3x^2-4x-3}{x^2+x}}\).