Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter

    Simple question relly but I can only get half of it...

    Solve this inequality:
    2/(x^2 - 1) > 1
    I get that re-arranging to 0 > x^2 -3
    x can be + or - square root 3

    but also + or - 1 is a solution but how do you show this?

    The solution to inequalities is normally a range of values, or several ranges.

    You have to be careful not to multiply by something (like (x^2-1)) that may be either positive or negative.

    So you could start by saying 2/(x^2-1) - 1 > 0 it helps to get a 0 on the RHS

    Put everything over a common denominator; factorise numerator and denominator

    Now it depends on your taught method. You can sketch. Or you can build a table of 'critical values' at which one factor changes sign. And then break x into those ranges, consider each one separately and think hard about boundary values.
    • Community Assistant
    • Study Helper

    Community Assistant
    Study Helper
    Since the sign of (x^2-1) is not the same for different values of x, it's best not to multiply both sides by (x^2-1).

    Instead, bring the 1 to the LHS and form one fraction:

    \displaystyle \frac{2}{x^2-1}-1 > 0 \implies \frac{2}{x^2-1}-\frac{x^2-1}{x^2-1}\implies -\frac{(x+3)(x-3)}{(x+1)(x-1)}>0

    This inequality shows that you should look at the behaviour of the fraction around the points -3,-1,1,3 (x<-3, -3<x<-1 etc.) to find the solutions.
    • Thread Starter

    ahhh of course!! Thanks a lot!!
How are you feeling about your exams?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.