Solving rational inequalities

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practise With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practise on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/1
?
Intros
Lessons
  1. Introduction to solving rational inequalities

    i) What is a rational inequality?

    ii) How to solve rational inequality?

    iii) Section Overview

0/7
?
Examples
Lessons
  1. Solving Rational Inequalities With One Fraction

    Solve

    1. x5x+1\frac{x-5}{x+1} > 00
    2. x2+5x+6x216\frac{x^{2}+5x+6}{x^{2}-16} < 00
  2. Solving Rational Inequalities With Two Fractions

    Solve

    1. x3x+26\frac{x-3}{x+2} \leq 6
    2. 1x53xx5\frac{1}{x-5} \geq \frac{3x}{x-5}
    3. 2x\frac{2}{x} < x5x12\frac{x}{5x - 12}
  3. Solving Rational Inequalities With Three Fractions

    Solve

    1. 53x4x19\frac{5}{3x} - \frac{4}{x} \geq \frac{1}{-9}
    2. 2yy212y+1+1y1\frac{2y}{y^{2}-1} \geq \frac{2}{y+1} + \frac{1}{y-1}
Topic Notes
?

Steps to solving rational inequalities:

1. Rewrite in the form p(x)q(x)\frac{p(x)}{q(x)} > 00 (symbol can be different)

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

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