Hey there! Sign in to join this conversationNew here? Join for free

Maths C3 - Simplifying Algebraic Fractions...Help with tricky Question? Watch

    • Thread Starter
    Offline

    18
    ReputationRep:
    Ok so I've just spent a long time trying to work out Exercise 1C question m from the Edexcel C3 Modular textbook. I managed to solve the answer but took so many steps to get it! There must be a quicker way to solve this question. The question is...

    Question m..:
    \frac{3}{x^2+3x+2}-\frac{2}{x^2+4x+4}

    The steps I took to work out the answer are as follows...
    \frac{3}{(x+1)(x+2)}-\frac{2}{(x+2)(x+2)}
    ...
    \frac{3x^2+12x+12}{(x+1)(x+2)^3}-\frac{2x^2+6x+4}{(x+1)(x+2)^3}
    ...
    \frac{x^2+6x+8}{(x+1)(x+2)^3}
    ...
    \frac{(x+2)(x+4)}{(x+1)(x+2)^3}
    ...
    \frac{x+4}{(x+1)(x+2)^2}
    • Community Assistant
    Offline

    18
    ReputationRep:
    Community Assistant
    (Original post by Philip-flop)
    Ok so I've just spent a long time trying to work out Exercise 1C question m from the Edexcel C3 Modular textbook. I managed to solve the answer but took so many steps to get it! There must be a quicker way to solve this question. The question is...

    Question m..:
    \frac{3}{x^2+3x+2}-\frac{2}{x^2+4x+4}

    The steps I took to work out the answer are as follows...
    \frac{3}{(x+1)(x+2)}-\frac{2}{(x+2)(x+2)}
    ...
    \frac{3x^2+12x+12}{(x+1)(x+2)^3}-\frac{2x^2+6x+4}{(x+1)(x+2)^3}
    ...
    \frac{x^2+6x+8}{(x+1)(x+2)^3}
    ...
    \frac{(x+2)(x+4)}{(x+1)(x+2)^3}
    ...
    \frac{x+4}{(x+1)(x+2)^2}
    Use a common denominator of  (x+1)(x+2)^2 instead of
    (x+1)(x+2)^3
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by NotNotBatman)
    Use a common denominator of  (x+1)(x+2)^2 instead of
    (x+1)(x+2)^3
    How did you figure out the common denominator so easily?
    Please explain as I'm terrible at working out common denominators
    Offline

    21
    ReputationRep:
    (Original post by Philip-flop)
    How did you figure out the common denominator so easily?
    Please explain as I'm terrible at working out common denominators
    When you had the original question, with the two fractions you can factorise both the quadratics on the bottom. Start with that and see where you can go.
    • Community Assistant
    Offline

    18
    ReputationRep:
    Community Assistant
    (Original post by Philip-flop)
    How did you figure out the common denominator so easily?
    Please explain as I'm terrible at working out common denominators
    You don't need (x+2)^3 as (x+2) is a factor of (x+2)^2 it's the same with numbers, you're looking for the lowest common multiple.
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    Community Assistant
    Welcome Squad
    (Original post by Philip-flop)
    How did you figure out the common denominator so easily?
    Please explain as I'm terrible at working out common denominators
    You just do it by inspection. Look what you need in order to make the denominators the same and that's it. Practice some more questions and you'll start to recognise them quicker.
    • Thread Starter
    Offline

    18
    ReputationRep:
    Oh yeah, I think I was just having a daft moment. Here is my new answer...

    Question m..:
    \frac{3}{x^2+3x+2}-\frac{2}{x^2+4x+4}

    New answer...
    \frac{3}{(x+1)(x+2)}-\frac{2}{(x+2)(x+2)}
    ...
    \frac{3(x+2)}{(x+1)(x+2)^2}-\frac{2(x+1)}{(x+1)(x+2)^2}
    ...
    \frac{(3x+6)-(2x+2)}{(x+1)(x+2)^2}
    ...
    \frac{x+4}{(x+1)(x+2)^2}

    Thank you everyone in this thread who helped. I'm really grateful. Took me a while to realise how stupid I was being :/
    Offline

    10
    ReputationRep:
    (Original post by Philip-flop)
    How did you figure out the common denominator so easily?
    Please explain as I'm terrible at working out common denominators
    Seems you have a gap somewhere in your knowledge...

    Watch these videos:
    https://www.youtube.com/watch?v=moLdgkGjrWI
    https://www.youtube.com/watch?v=mRSgfo6hZlo

    Never be afraid to revisit the basics...
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by Naruke)
    Seems you have a gap somewhere in your knowledge...

    Watch these videos:
    https://www.youtube.com/watch?v=moLdgkGjrWI
    https://www.youtube.com/watch?v=mRSgfo6hZlo

    Never be afraid to revisit the basics...
    Yes. You're probably right. As I'm self-taught it's likely I have missed something important

    Thanks for the videos. I will check them out now
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by NotNotBatman)
    You don't need (x+2)^3 as (x+2) is a factor of (x+2)^2 it's the same with numbers, you're looking for the lowest common multiple.
    Thank you so much for your help. I've realised that I need to top up on my knowledge of LCM.

    (Original post by RDKGames)
    You just do it by inspection. Look what you need in order to make the denominators the same and that's it. Practice some more questions and you'll start to recognise them quicker.
    Thank you. You definitely helped me figure out my obvious mistake
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brexit voters: Do you stand by your vote?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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.