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Math Help - Is this Complex Rational Expression right?

  1. #1
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    Is this Complex Rational Expression right?

    (x+5)(x-2) - (x+5)(x+1)
    ---------- ----------
    (x+5)(x+1) (x+5)(x-2)
    --------------------------
    (x+5)(x+1) - (x+5)(x-2)
    ----------- -----------
    (x+5)(x-2) (x+5)(x+1)

    So I factor them than I multiply times the LCD which (x+5)(x+1)(x-2)

    I got this.

    (x+5)(x-2)(x-2) - (x+5)(x+1)(x+1)
    -----------------------------------
    (x+5)(x+1)(x+1) - (x+5)(x-2)(x-2)

    Than I subtracted like terms (x+5) which left me with this.

    (x-2)(x-2)(x+1)(x+1)
    ---------------------
    (x+1)(x+1)(x-2)(x-2)

    I cancel like terms which is everything so I got this

    1
    --- = 1
    1

    What do you guys think does that look right?
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  2. #2
    Member arpitagarwal82's Avatar
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    Quote Originally Posted by carlos_gaona_17 View Post
    (x+5)(x-2) - (x+5)(x+1)
    ---------- ----------
    (x+5)(x+1) (x+5)(x-2)
    --------------------------
    (x+5)(x+1) - (x+5)(x-2)
    ----------- -----------
    (x+5)(x-2) (x+5)(x+1)

    So I factor them than I multiply times the LCD which (x+5)(x+1)(x-2)

    I got this.

    (x+5)(x-2)(x-2) - (x+5)(x+1)(x+1)
    -----------------------------------
    (x+5)(x+1)(x+1) - (x+5)(x-2)(x-2)

    Than I subtracted like terms (x+5) which left me with this.

    (x-2)(x-2)(x+1)(x+1)
    ---------------------
    (x+1)(x+1)(x-2)(x-2)


    I cancel like terms which is everything so I got this

    1
    --- = 1
    1

    What do you guys think does that look right?
    Red part has error above
    It should be
    (x-2)(x-2) - (x+1)(x+1)
    ---------------------
    (x+1)(x+1)(x-2)(x-2)


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


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


    = 3/(x+1)^2(x-2)^2
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  3. #3
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    Where did you get that 3 from?
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  4. #4
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    Quote Originally Posted by carlos_gaona_17 View Post
    Where did you get that 3 from?
    You can't cancel across addition or subtraction signs.

    So to simplify the top you'd have to expand and collect like terms.

    I however, get as my final answer

    \frac{-6x + 3}{(x - 2)^2(x + 1)^2}.
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  5. #5
    Member arpitagarwal82's Avatar
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    carlos_gaona_17 you just messed up in typing the question.
    please use Latex while typing the mathematical expressions in this forum.

    If you take LCM, your expression will reduce to
    ((x - 2)^2 - (x + 1)^2))/((x + 1)^2 - (x - 2)^2)
    = -1
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