? asked in 科學及數學數學 · 1 decade ago

MATHS~~20POINTS

SIMPLIFY

1. (2x/x^2-1)-(1/x-1)-(1/x+1)

2. a= 1-x^2 b=1+x express 4 in terns of b

3.(5x+2)[(5x/2) -1]

2 Answers

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  • 1 decade ago
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    1. (2x/x^2-1)-(1/x-1)-(1/x+1)

    = 2/x - 1 - 1/x + 1 - 1/x - 1

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

    = 0-1+1-1

    = -1

    2. a= 1-x^2

    b=1+x

    express 4 in terns of b (i suppose u are asking "express a in terms of b")

    b = 1+x

    b-1 = 1+x-1

    x = b-1

    a = 1-x^2

    = 1 - (b-1)^2

    = 1 - [b^2 - 2(b)(1) + (-1)]

    = 1 -b^2 + 2b + 1

    = -b^2 + 2b + 2

    So, a = -b^2 + 2b + 2.

    3.(5x+2)[(5x/2) -1]

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

    = (25x^2)/2 -5x + 5x - 2

    = (25x^2)/2 - 2

    2008-10-19 21:30:27 補充:

    a = 1-x^2

    = 1 - (b-1)^2

    = 1 - [b^2 - 2(b)(1) + (-1)] <-- sorry i made mistake here

    = 1 - b^2 + 2b + 1

    = -b^2 + 2b + 2

    So, a = -b^2 + 2b + 2.

    should be

    = 1 - [b^2 - 2(b)(1) + (-1)^2]

    = 1 - b^2 + 2b - 1

    = - b^2 + 2b

    So, a in terms of b is - b^2 + 2b. =)

  • 1 decade ago

    (2x/x^2-1)-(1/x-1)-(1/x+1)

    =[2x-(x+1)-(x-1)]/(x^2-1)

    =(2x-x-1-x+1)/(x^2-1)

    =0//

    a= 1-x^2 b=1+x express a in terns of b

    a= 1-x^2

    x=sqrt(1-a)

    then sub x=sqrt(1-a) into b=1+x

    b=sqrt(1-a)+1//

    (5x+2)[(5x/2) -1]

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

    =(25x^2-4)/2//

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