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Math Help - Simplifying and factorising

  1. #1
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    Simplifying and factorising

    1)Simplify \frac{1}{2-11x+12x^2}-\frac{1}{12x^2-5x-2}

    2)Factorise 49x^2-64(y-x)^2

    For the first question, My attempt is:
    \frac{12x^2-5x-2-2+11x-12x^2}{(2-11x+12x^2)(12x^2-5x-2)}
    =\frac{6x-4}{(2-11x+12x^2)(12x^2-5x-2)}

    I am confused at deciding on how to start the second question....
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Punch View Post
    1)Simplify \frac{1}{2-11x+12x^2}-\frac{1}{12x^2-5x-2}

    2)Factorise 49x^2-64(y-x)^2

    For the first question, My attempt is:
    \frac{12x^2-5x-2-2+11x-12x^2}{(2-11x+12x^2)(12x^2-5x-2)}
    =\frac{6x-4}{(2-11x+12x^2)(12x^2-5x-2)}

    I am confused at deciding on how to start the second question....
    1) can be further simplified

    \frac{12x^2-12x^2+11x-5x-2-2}{[(4x-1)(3x-2)][(4x+1)(3x-2)]}

    =\frac{6x-4}{[(4x-1)(3x-2)][(4x+1)(3x-2)]}=\frac{2(3x-2)}{[(4x-1)(3x-2)][(4x+1)(3x-2)]}

    =\frac{2}{(4x-1)(4x+1)(3x-2)}

    2)

    This is the difference of squares.

    49x^2-64(y-x)^2=(7x)^2-[8(y-x)]^2=[7x-8(y-x)][7x+8(y-x)]

    =[7x-8y+8x][7x+8y-8x]=[15x-8y][8y-x]
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