Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Ok, so have the following partial fraction:

    X^2 + X + 1
    (X-1)(X+1)(X^2 -1)

    which is
    A/(X+1) + B/(X-1) + (Cx + D)/(X^2 +1)

    By putting x=1 and x=-1 in, can work out B=3/4 and A=-1/4, but then where do you go? Am I on the right tracks?

    Any help would be much appreciated!
    Offline

    2
    ReputationRep:
    You are on the right tracks. For the next bit you need to compare co-efficients.

    You know that:

    x^2 + x + 1 = A(x-1)(x^2+1) + B(x+1)(x^2+1) + (Cx+D)(x+1)(x-1)

    You already know what A and B are. You know that he coefficient of x^2 on the right-hand side must be 1 and the coefficient of x on the r.h.s. must be 1 and the constant on the r.h.s. must be 1. So now you just need to work out what values of C and D will make this so.

    EDIT - And, of course, the 'co-efficient' of x^3 must be zero.
    • TSR Group Staff
    Offline

    20
    ReputationRep:
    TSR Group Staff
    Alternatively, you could try putting in another number, chosen at semi-random. Good ones to try are 1, 0, -1, and possibly 2, if none of the others are any use.

    x2 + x + 1 = A/(x+1) + B/(x-1) + (Cx + D)/(x2+1)

    Let x = 0,

    1 = A - B + C + D
    1 = -1/4 - 3/4 + C + D
    1 = -1 + C + D
    2 = C + D

    In this case, because you've got two variables, you need to find yet another equation and solve them simultaneously. It is at this point that you want to give up hope and go with comparing coefficients instead :P. Using an arbitary substitution does help sometimes though.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thanks guys!!!
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 23, 2006

University open days

  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
  • Bournemouth University
    Undergraduate Mini Open Day Undergraduate
    Wed, 9 Jan '19
Poll
Did you get less than your required grades and still get into university?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

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