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Ray
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Ray asked in 科學及數學數學 · 1 decade ago

F4 Maths Dividing Polynomials3

2 Answers

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  • 1 decade ago
    Favorite Answer

    (1) (x - 8)/(x - 4) + (x - 5)/(x - 7) - 2

    = (x - 4 - 4)/(x - 4) + (x - 7 + 2)/(x - 7) - 2

    = [1 - 1/(x - 4)] + [1 + 2/(x - 7)] - 2

    = 2/(x - 7) - 1/(x - 4)

    (2) 2a/(a - 1) - (a - 1)/(a + 1) - (a + 1)/a

    = [2(a - 1) + 2]/(a - 1) - (a + 1 - 2)/(a + 1) - 1 - 1/a

    = 2 + 2/(a - 1) - 1 + 2/(a + 1) - 1 - 1/a

    = 2/(a - 1) + 2/(a + 1) - 1/a

    (3) (x + 2)/(x + 1) - (x + 3)/(x + 2) - (x + 5)/(x + 4) + (x + 6)/(x + 5)

    = (x + 1 + 1)/(x + 1) - (x + 2 + 1)/(x + 2) - (x + 4 + 1)/(x + 4) + (x + 5 + 1)/(x + 5)

    = 1 + 1/(x + 1) - 1 - 1/(x + 2) - 1 - 1/(x + 4) + 1 + 1/(x + 5)

    = 1/(x + 1) - 1/(x + 2) - 1/(x + 4) + 1/(x + 5)

    Source(s): Myself
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  • 1 decade ago

    1.(x-8)/(x-4)+(x-5)/(x-7)-2

    =[(x-8)(x-7)+(x-5)(x-4)]/[(x-4)(x-7)]-2

    =(-24x+76)/[(x-4)(x-7)]-2

    =(-x^2-2x+20)/(x-4)(x-7)

    =-2(x-10)/[(x-4)(x-7)]//

    2.2a/(a-1)-(a-1)/(a+1)-(a+1)/a

    =(3 a^2+1)/((a-1) a (a+1))//

    3.(x+2)/(x+1)-(x+3)/(x+2)-(x+5)/(x+4)+(x+6)/(x+5)

    =(6 (x+3))/((x+1) (x+2) (x+4) (x+5))

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