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Math Help - Algebra...Adding & Subtracting Fractions

  1. #1
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    Algebra...Adding & Subtracting Fractions

    Add or subtract as indicated.

    1. b/b-1 + 2b/b^2 -1

    2. a-1/a+1 + a+1/a-1

    Please help me to understand how to find these answers. Thanks!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cutiepi_86 View Post
    1. b/b-1 + 2b/b^2 -1
    I presume this is
    b/(b - 1) + 2b/(b^2 - 1)

    Please use parenthesis!

    Like adding any other kind of fraction, you need a common denominator. So factor
    b^2 - 1 = (b + 1)(b - 1)

    The first fraction only has a b - 1 in its denominator, so we need to multiply top and bottom by b + 1:

    b/(b - 1) * (b + 1)/(b + 1) + 2b/[(b + 1)(b - 1)]

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

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

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

    = [b^2 + 3b]/[(b + 1)(b - 1)]

    = [b(b + 3)]/[(b + 1)(b - 1)]

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cutiepi_86 View Post
    Add or subtract as indicated.

    1. b/b-1 + 2b/b^2 -1

    2. a-1/a+1 + a+1/a-1

    Please help me to understand how to find these answers. Thanks!
    Again, this is
    (a - 1)/(a + 1) + (a + 1)/(a - 1)
    right?

    To get a common denominator, we need to multiply the first fraction by (a - 1)/(a - 1) and the second fraction by
    (a + 1)/(a + 1):

    (a - 1)/(a + 1) * (a - 1)/(a - 1) + (a + 1)/(a - 1) * (a + 1)/(a + 1)

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

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

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

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

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

    -Dan
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  4. #4
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    Thanks so much Dan!
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