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    Hi, we've been given work to do over the holidays by our subject teachers and i seem to be totally stuck by a few of the maths questions. Could someone please help me?


    Simplify:

    1)  \frac {x^2 - 1}{x + 1}


    2)  \frac {4y^2 - 9}{4y + 6}


    3)  \frac {8yx}{6x^3y^2-4xy^2}



    Express as a single fraction:

    1)  \frac {4}{x^2} - \frac {5}{x}


    2)  \frac {1}{ab} + \frac {1}{ac} + \frac {1}{bc}



    Solve using the formula:

    1)  x^2 + 7x + 2 = 0


    2)  10y^2 - 6y - 15 = 0


    3)  \frac {a+2}{a} = \frac {a}{2a-5}


    Thanks for any help =)
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    Despite the fact that I feel I'm doing someone's homework for them:

    first 3 questions - you need to factorise either the top and the bottom and then cancel down

    Middle 2 - just treat these as though you were adding normal fractions and find a common denominator.

    Last 3 - use the quadratic formula.
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    For simplify 1 and 2 you need to factorize the top of the fraction. Bear in mind that (a+b)(a-b)=a2-b2.

    For the third simplify you need to factorize the bottom by taking out common factors. A simpler example would be
    2ab/(a2b+b2a)=
    2ab/ab(a+b)=
    2/(a+b)

    For the express as a single fraction questions you need to put them over a common denominator (have the same thing at the bottom of all of them). If you were to have
    \frac{2}{3}-\frac{1}{5}
    then you would make the new denominator the lowest common multiple of the current denominators:
    \frac{10}{15}-\frac{3}{15}=\frac{7}{15}

    The first two solves are quadratics. The easiest way to solve these would be using the quadratic formula. If you have learnt how to complete the square you may want to solve them that way instead. Neither of them factorise nicely.

    In the third solve you need to get rid of the fractions. If you have
    \frac{a}{m}=\frac{b}{n}
    then
    an=bm
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    Thanks harr and studienka =)
 
 
 
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Updated: August 16, 2007

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