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    I've got most of the things we need in algebra apart from these fraction type questions it would seem.

    1. Solve the equation: x+2/2 = 2x


    2. Simplify: x^2-3x/x^2-9


    3. Solve: 4/x-1 = 3/2x+1

    4. Simplify fully: 4x^2-14x/6x-21

    / = Over
    ^= To the power of!

    Thank you sooo much for any help.
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    1. Start by multiplying both sides by two

    2. Do you know about the difference of two squares. Have a go at factorising the top and bottom and see what you get

    3. Any ideas on how to get the x-terms on top? Once they're on top it'll be much easier

    4. Try factorising the numerator and denominator. See what both terms on the top of bottom have in common and take that outside a bracket.
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    1. Solve the equation: x+2/2 = 2x

    Hint: times both sides by two
    Spoiler:
    Show

    x+2=4x
    2=3x
    x=2/3


    2. Simplify: x^2-3x/x^2-9

    Hint: factorise x^2-3x
    Spoiler:
    Show
    x^2-3x=x(x-3)

    Hint2: factorise x^2-9 by completing the square
    Spoiler:
    Show
    x^2-9=(x+3)(x-3)

    Hint3: divide through by (x-3)
    Spoiler:
    Show
    \displaystyle \frac{x(x-3)}{(x+3)(x-3)}=\frac{x}{x+3}


    Try and do the last two yourself
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    1. If you times both sides by 2 you should get a normal algebra equation.

    2. If you factorize the top (common factor) and factorize the bottom (difference of two squares) then something should cancel out.

    3. Multiply both sides of the equation by the two denominators. This will cancel out the denominators on both sides and leave a normal equation for you to solve.

    4. Like number two, factorise the top and bottom but note that this time they both have common factors (there is no difference of two squares.)

    Hope this gives you a push in the right direction.
 
 
 
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Updated: November 15, 2008

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