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Algebraic Fraction

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    I got the answer to be -7 over -3 is that correct

    thanks.
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    No, that's not right. Post your working.
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    I believe the answer is: \frac{2x^2 - 7}{x (2x - 3)}

    Post your working so we can see what the problem is.
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    2x(x)-7/x(2x-3)x(2x-3)
    2x^2-7/2x^2-3
    2x^2 cancels out so you're left with -7/-3
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    (Original post by AtomSmasher)
    I believe the answer is: \frac{2x^2 - 7}{x (2x - 3)}

    Post your working so we can see what the problem is.
    Oh now I see where I have gone wrong.

    I shouldn't have multiplied out the denominator.
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    (Original post by zed963)
    2x^2-7/2x^2-3
    2x^2 cancels out so you're left with -7/-3
    You cannot cancel terms in a fraction, only factors. 2x^2 is not a factor of the numerator or the denominator.

    Please let me know if you're not confident with this and I could explain further or give you some questions.
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    (Original post by zed963)
    2x(x)-7/x(2x-3)x(2x-3)
    2x^2-7/2x^2-3
    2x^2 cancels out so you're left with -7/-3
    I the denominator is meant to be 2x^2 - 3x.
    Remember, you can only cancel out common factors and since 2x^2 isn't a factor you can't cancel it out.
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    (Original post by AtomSmasher)
    I the denominator is meant to be 2x^2 - 3x.
    Remember, you can only cancel out common factors and since 2x^2 isn't a factor you can't cancel it out.
    But if I expand the top I get 2x^2 and in the the denominator it is the same so why can't I cancel them out.
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    (Original post by notnek)
    You cannot cancel terms in a fraction, only factors. 2x^2 is not a factor of the numerator or the denominator.

    Please let me know if you're not confident with this and I could explain further or give you some questions.
    Sure give me some questions.
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    This is a very common misconception and it is terribly wrong. I suggest you take notnek up on his offer if you don't understand why your attempt doesn't work.
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    (Original post by zed963)
    Sure give me some questions.
    Ok first you must realise the difference between "terms" and "factors". A term is something in algebra which is separated from other things by either + or -.

    e.g. 3xy+2x

    The two terms here are 3xy and 2x.

    A factor is something which is part of a product.

    e.g. 3xy + 2x

    In the first term, the factors are 3, x and y. And in the second term, the factors are 2 and x.

    When cancelling algebraic fractions, you can only do it if the thing that you want to cancel is a factor of both the numerator and the denominator.

    e.g. \displaystyle \frac{x(x+2)}{x}

    x is a factor of the whole of the numerator and is also a factor of the denominator so you cancel it to get:

    \displaystyle \frac{x+2}{1}=x+2

    Next example:

    \displaystyle \frac{2xy+3}{2xy(3z)}

    There are two terms on the numerator, 2xy and 3. 2xy is not a factor of the numerator. 2xy is a factor of the denominator but it has to be a factor of both in order to cancel. So you would leave this fraction as it is.

    Now try simplifying these fractions:

    a) \displaystyle \frac{3(x+5)(x+2)}{2(x+2)}

    b) \displaystyle \frac{3x+2z}{2z}

    c) \displaystyle \frac{3(x+3)+5}{(x+3)(x+2)}

    d) \displaystyle \frac{3(x+2)+2(x+2)}{(x+2)(x+1)}

    For d), try simplifying the numerator.
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    (Original post by zed963)
    But if I expand the top I get 2x^2 and in the the denominator it is the same so why can't I cancel them out.
    You can only cancel them out if they are factors, i.e., when multiplied by something else (not added or subtracted from) it makes the expression. You know all about factorising right?

    I'll just do a very simple example, it always helps: You can factorise \frac{4x}{6x} to \frac{2 \times 2x}{3 \times 2x}. Since 2x is a common factor you can cancel it out, getting \frac{2}{3}. However, you can express the same fraction as \frac{2x + 2x}{4x + 2x}, but since these are not factors, you can't cancel them out. If you tried cancelling them, you'd end up with \frac{2x}{4x}, which obviously isn't the same.

    Sorry if this seems like a kind of childish explanation, I'm sure you know what I mean though?
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    (Original post by notnek)
    Ok first you must realise the difference between "terms" and "factors". A term is something in algebra which is separated from other things by either + or -.

    e.g. 3xy+2x

    The two terms here are 3xy and 2x.

    A factor is something which is part of a product.

    e.g. 3xy + 2x

    In the first term, the factors are 3, x and y. And in the second term, the factors are 2 and x.

    When cancelling algebraic fractions, you can only do it if the thing that you want to cancel is a factor of both the numerator and the denominator.

    e.g. \displaystyle \frac{x(x+2)}{x}

    x is a factor of the whole of the numerator and is also a factor of the denominator so you cancel it to get:

    \displaystyle \frac{x+2}{1}=x+2

    Next example:

    \displaystyle \frac{2xy+3}{2xy(3z)}

    There are two terms on the numerator, 2xy and 3. 2xy is not a factor of the numerator. 2xy is a factor of the denominator but it has to be a factor of both in order to cancel. So you would leave this fraction as it is.

    Now try simplifying these questions:
    Okay
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    (Original post by AtomSmasher)
    You can only cancel them out if they are factors, i.e., when multiplied by something else (not added or subtracted from) it makes the expression. You know all about factorising right?

    I'll just do a very simple example, it always helps: You can factorise \frac{4x}{6x} to \frac{2 \times 2x}{3 \times 2x}. Since 2x is a common factor you can cancel it out, getting \frac{2}{3}. However, you can express the same fraction as \frac{2x + 2x}{4x + 2x}, but since these are not factors, you can't cancel them out. If you tried cancelling them, you'd end up with \frac{2x}{4x}, which obviously isn't the same.

    Sorry if this seems like a kind of childish explanation, I'm sure you know what I mean though?
    Yeah .
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    (Original post by notnek)
    Ok first you must realise the difference between "terms" and "factors". A term is something in algebra which is separated from other things by either + or -.

    e.g. 3xy+2x

    The two terms here are 3xy and 2x.

    A factor is something which is part of a product.

    e.g. 3xy + 2x

    In the first term, the factors are 3, x and y. And in the second term, the factors are 2 and x.

    When cancelling algebraic fractions, you can only do it if the thing that you want to cancel is a factor of both the numerator and the denominator.

    e.g. \displaystyle \frac{x(x+2)}{x}

    x is a factor of the whole of the numerator and is also a factor of the denominator so you cancel it to get:

    \displaystyle \frac{x+2}{1}=x+2

    Next example:

    \displaystyle \frac{2xy+3}{2xy(3z)}

    There are two terms on the numerator, 2xy and 3. 2xy is not a factor of the numerator. 2xy is a factor of the denominator but it has to be a factor of both in order to cancel. So you would leave this fraction as it is.

    Now try simplifying these fractions:

    a) \displaystyle \frac{3(x+5)(x+2)}{2(x+2)}

    b) \displaystyle \frac{3x+2z}{2z}

    c) \displaystyle \frac{3(x+3)+5}{(x+3)(x+2)}

    d) \displaystyle \frac{3(x+2)+2(x+2)}{(x+2)(x+1)}

    For d), try factorising the numerator.
    For a) 3x+15/2
    b) 3x
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    (Original post by zed963)
    For a) 3x+15/2(x+2)
    No, try again.
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    (Original post by raheem94)
    No, try again.
    3x+15/2
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    (Original post by zed963)
    3x+15/2
    :yep:
    :congrats:
  19. Offline

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    (Original post by raheem94)
    :yep:
    :congrats:
    For b) 3x
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    (Original post by zed963)
    3x+15/2
    Remember you should write it as (3x+15)/2, otherwise it is ambiguous.

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