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- AU Year 12 Maths
- Rational Functions

Still Confused?

Try reviewing these fundamentals first

Still Confused?

Try reviewing these fundamentals first

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Get Started Now- Intro Lesson10:28
- Lesson: 1a8:32
- Lesson: 1b9:48
- Lesson: 2a10:39
- Lesson: 2b6:05
- Lesson: 2c11:51
- Lesson: 3a8:03
- Lesson: 3b9:27

Basic Concepts: Solving polynomial inequalities

Related Concepts: Solving rational equations

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

- Introduction
__Introduction to solving rational inequalities__i) What is a rational inequality?

ii) How to solve rational inequality?

iii) Section Overview

- 1.
**Solving Rational Inequalities With One Fraction**Solve

a)$\frac{x-5}{x+1}$ > $0$b)$\frac{x^{2}+5x+6}{x^{2}-16}$ < $0$ - 2.
**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)$\frac{2}{x}$ < $\frac{x}{5x - 12}$ - 3.
**Solving Rational Inequalities With Three Fractions**Solve

a)$\frac{5}{3x} - \frac{4}{x} \geq \frac{1}{-9}$b)$\frac{2y}{y^{2}-1} \geq \frac{2}{y+1} + \frac{1}{y-1}$