Join TSR now and get all your revision questions answeredSign up now
    • Thread Starter
    Offline

    3
    ReputationRep:
    Hi please could someone help with exercise 4.1 part b)? I've got the denominator factorised as x(x^2+2x+5) but not sure how to split the fraction into partial fractions.
    Attached Images
     
    • Community Assistant
    • Welcome Squad
    Online

    17
    ReputationRep:
    (Original post by jordanwu)
    Hi please could someone help with exercise 4.1 part b)? I've got the denominator factorised as x(x^2+2x+5) but not sure how to split the fraction into partial fractions.
    So it would be in the form \displaystyle \frac{A}{x}+\frac{Bx+C}{x^2+2x+5  }
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by TeeEm)
    A/x +(Bx + C)/(x^2+2x+5), as the denominator is irreducible
    I ended up with -1/x + 4x/x^2+2x+5, where should I go on from here?
    • Community Assistant
    • Welcome Squad
    Online

    17
    ReputationRep:
    (Original post by jordanwu)
    I ended up with -1/x + 4x/x^2+2x+5, where should I go on from here?
    Integrate the first fraction which should be straightforward.

    Then if you express the second one as:

    \displaystyle 2\int \frac{2x}{x^2+2x+5}.dx =2\int \frac{(2x+2)-(2)}{x^2+2x+5}.dx

    \displaystyle =2\int \frac{2x+2}{x^2+2x+5}.dx + 2\int \frac{-2}{x^2+2x+5}.dx

    which is straight forward as well.
 
 
 
Poll
If you won £30,000, which of these would you spend it on?
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

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