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Math Help - Simplifying question

  1. #1
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    Simplifying question

    Hello everyone,
    This question is one of the basic simplifying questions which i couldn't understand.

    Lets take this as an example:
    1/x + 2/(x+1)

    At some point we will get 3x+1/x(x+1)

    My question is...in simplifying fractions why do we open brackets if they on top but we don't open them if they are in the denominator's place ?

    Thanks
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  2. #2
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    Re: Simplifying question

    Quote Originally Posted by Mathbeg View Post
    Hello everyone,
    This question is one of the basic simplifying questions which i couldn't understand.

    Lets take this as an example:
    1/x + 2/(x+1)

    At some point we will get 3x+1/x(x+1)

    My question is...in simplifying fractions why do we open brackets if they on top but we don't open them if they are in the denominator's place ?

    Thanks
    Hi Mathbeg,

    Of course you could open the brackets and write the answer if you like. There is nothing wrong with it.
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  3. #3
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    Re: Simplifying question

    Quote Originally Posted by Sudharaka View Post
    Hi Mathbeg,

    Of course you could open the brackets and write the answer if you like. There is nothing wrong with it.
    Oh, my teacher told me it would be wrong.
    maybe he meant wrong for GCSE only.
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  4. #4
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    Re: Simplifying question

    Quote Originally Posted by Mathbeg View Post
    Oh, my teacher told me it would be wrong.
    maybe he meant wrong for GCSE only.
    He was probably referring to the markscheme. Generally it's better to have things factored with fractions for GCSE exams. It's good practice for things like series, integration, proofs, inequalities and so forth later on when having factored numerators/denominators can make life very simple.
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  5. #5
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    Re: Simplifying question

    You need to get the denominator the same in each fraction before you can add. So, 1/x becomes 1(x+1)/x(x+1), and 2/(x+1) becomes 2(x)/x(x+1). At this point you can add the fractions being that the denominator in each is the same. So, what is 1(x+1) + 2(x)?
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  6. #6
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    Re: Simplifying question

    Quote Originally Posted by Mathbeg View Post
    3x+1/x(x+1)
    I don't understand your question (what's opening a bracket?!) but
    above should be: (3x + 1) / (x(x + 1))

    9 + 6/3 = 9 + 2 = 11
    (9 + 6)/3 = 15/3 = 5
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  7. #7
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    Re: Simplifying question

    1/x + 2/(x+1)
    1(x+1) + 2 (x) why does this become 3x + 1 but the denominator stays x(x+1) instead of X^2 + X
    I mean the numerator while not have brackets but the deno will
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  8. #8
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    Re: Simplifying question

    Quote Originally Posted by Mathbeg View Post
    1(x+1) + 2 (x) why does this become 3x + 1
    1(x+1) + 2 (x) = x + 1 + 2x = 3x + 1
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  9. #9
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    Re: Simplifying question

    Looks like my question is confusing.

    What i mean is: The numerator 1(x+1) + 2(x) why dont we keep it as it is as we did in the denominator ? the deno will be x(x+1) at the end, why not write x^2 + x as we did for the 1(x+1)..... in the numerator ?
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  10. #10
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    Re: Simplifying question

    Quote Originally Posted by Mathbeg View Post
    ....why not write x^2 + x as we did for the 1(x+1).....
    You could, but then it would be considered "not fully factored"; depends on original
    problem statement ; 3x + 1 cannot be factored further, x^2 + x can.
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