# Solving rational inequalities

### Solving rational inequalities

#### Lessons

Steps to solving rational inequalities:

1. Rewrite in the form $\frac{p(x)}{q(x)}$ > $0$ (symbol can be different)

2. Solve $p(x) = 0$ and $q(x) = 0$

3. Put answers from step 2 on a number line and check end points and test values

• 1.
Introduction to solving rational inequalities

i) What is a rational inequality?

ii) How to solve rational inequality?

iii) Section Overview

• 2.
Solving Rational Inequalities With One Fraction

Solve

a)
$\frac{x-5}{x+1}$ > $0$

b)
$\frac{x^{2}+5x+6}{x^{2}-16}$ < $0$

• 3.
Solving Rational Inequalities With Two Fractions

Solve

a)
$\frac{x-3}{x+2} \leq 6$

b)
$\frac{1}{x-5} \geq \frac{3x}{x-5}$

c)
$\frac{2}{x}$ < $\frac{x}{5x - 12}$

• 4.
Solving Rational Inequalities With Three Fractions

Solve

a)
$\frac{5}{3x} - \frac{4}{x} \geq \frac{1}{-9}$

b)
$\frac{2y}{y^{2}-1} \geq \frac{2}{y+1} + \frac{1}{y-1}$