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Math Help - Trying to Factorise/Simplify an Algebraic Fraction

  1. #1
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    Trying to Factorise/Simplify an Algebraic Fraction

    Hello there sorry If I've posted this in the wrong forum but I've been having trouble with this one question in a textbook and I'd be very greatful if someone could help me through it The question is -
    Simplify:

    ___(4x^2 - y^2) X (x^2 + 2xy)__
    (2x^2 + 3xy - 2y^2) X (xy - 2x^2)
    I Hope i've made sense it ain't the prettiest diagram but i think you can get the jist of it and just incase the X represents multiply and the ^ refer to powers. I think the base of my difficulty is when im trying to factorise and apply 2x^2 + 3xy - 2y^2 as it isnt your traditional 'ax^2 + bx + c' quadratic.

    So yeah I think thats about it, thanks for reading and I hope you can help
    Last edited by Supaweak; December 27th 2008 at 06:01 PM.
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  2. #2
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    \frac{(4x^2-y^2)(x^2+2xy)}{(2x^2 + 3xy - 2y^2)(xy - 2x^2)} = \frac{(2x-y)(2x+y)(x)(x+2y)}{(2x - y)(x + 2y)(x)(y-2x)}
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  3. #3
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    Quote Originally Posted by skeeter View Post
    \frac{(4x^2-y^2)(x^2+2xy)}{(2x^2 + 3xy - 2y^2)(xy - 2x^2)} = \frac{(2x-y)(2x+y)(x)(x+2y)}{(2x - y)(x + 2y)(x)(y-2x)}

    Hey thanks, could you tell me how you got from

    2x^2 + 3xy - 2y^2 to (2x - y)(x+2y)?

    Thanks!
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  4. #4
    Senior Member euclid2's Avatar
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    Quote Originally Posted by Supaweak View Post
    Hey thanks, could you tell me how you got from

    2x^2 + 3xy - 2y^2 to (2x - y)(x+2y)?

    Thanks!
    The same thing done to the numerator, factoring.

    2x^2+3xy-2y^2 = (2x-y)(x+2y)= 2x^2+4xy-xy-2y^2=2x^2+3xy-2y^2
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  5. #5
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    Ahh Thanks Heaps! Instead of splitting the 3xy into 4xy and -1xy I kept splitting it into 2xy and 1xy which wasnt working out for me, thanks again!
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