Turn on thread page Beta
    • Thread Starter
    Offline

    8
    ReputationRep:
    Express 1 − t^2 / t^2(1 + t 2) in partial fractions.

    So i got the whole A/t + B/t^2 + (Ct + D)/( t^2 + 1)

    Put t=0 and got B= 1. Now how do I get A C and D? If I put t=3, I get 3 variables and I just don't know how to get those three.

    Thanks
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by ChemBoy1)
    Express 1 − t^2 / t^2(1 + t 2) in partial fractions.

    So i got the whole A/t + B/t^2 + (Ct + D)/( t^2 + 1)

    Put t=0 and got B= 1. Now how do I get A C and D? If I put t=3, I get 3 variables and I just don't know how to get those three.

    Thanks
    Can you please post the identity you're considering i.e. the line of working after A/t + B/t^2 + (Ct + D)/( t^2 + 1) ?
    • Community Assistant
    Online

    20
    ReputationRep:
    Community Assistant
    (Original post by ChemBoy1)
    Express 1 − t^2 / t^2(1 + t 2) in partial fractions.

    So i got the whole A/t + B/t^2 + (Ct + D)/( t^2 + 1)

    Put t=0 and got B= 1. Now how do I get A C and D? If I put t=3, I get 3 variables and I just don't know how to get those three.

    Thanks
    Put t=-1 and t=1 then solve a system of 3 eqs in 3 variables
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by RDKGames)
    Put t=-1 and t=1 then solve a system of 3 eqs in 3 variables
    Comparing coefficients gets the answer quickly without the need for solving a system of equations.
    • Community Assistant
    Online

    20
    ReputationRep:
    Community Assistant
    (Original post by Notnek)
    Comparing coefficients gets the answer quickly without the need for solving a system of equations.
    So it does.
    Didn’t look at it for long enough.
    • Thread Starter
    Offline

    8
    ReputationRep:
    Is there not an easier way, it was only a 4 mark question, solving a 3 variable equation sees to much, is there not a simpler way?
    (Original post by RDKGames)
    Put t=-1 and t=1 then solve a system of 3 eqs in 3 variables
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by ChemBoy1)
    Is there not an easier way, it was only a 4 mark question, solving a 3 variable equation sees to much, is there not a simpler way?
    Yes, comparing coefficients as I mentioned above. Try it and post your working if you get stuck.
    • Community Assistant
    Online

    20
    ReputationRep:
    Community Assistant
    (Original post by ChemBoy1)
    Is there not an easier way, it was only a 4 mark question, solving a 3 variable equation sees to much, is there not a simpler way?
    Compare coefficients as said above.

    The simplest/quickest way to solve it is by saying:

    \dfrac{1-t^2}{t^2(1+t^2)} = \dfrac{(1+t^2) - 2t^2}{t^2(1+t^2)} = \dfrac{(1+t^2)}{t^2(1+t^2)}-\dfrac{2t^2}{t^2(1+t^2)}
    ...then cancel the common terms in both fractions to be left with the answer.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 17, 2018
Poll
Is the Big Bang theory correct?
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

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.