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College Algebra Question

  1. Aug 18, 2003 #1

    Cod

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    I recently started college and I'm in the first Math class, College Algebra. I'm having some problems with simplifying some basic functions if anyone can help me out.


    Problems like:

    Example 1: x^-2 - y^-2 / x^-1 + y^-1

    Example 2: x^-1 + y^-1 / (x+y)^-1



    If you noticed, I seem to be having problems with the problems involving negative squares. Any help on how to work these problems is greatly appreciated.
     
  2. jcsd
  3. Aug 18, 2003 #2
    Start by turning those negative rascals positive. That is, X^-1 becomes 1/X, etc. After you've done that take another look at your problem (it will be less confusing then) and decide on your next course of action.
     
    Last edited by a moderator: Aug 18, 2003
  4. Aug 18, 2003 #3

    Cod

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    So the correct answer would be:

    2y - 2x / y + x ??
     
  5. Aug 19, 2003 #4

    jcsd

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    I'm a bit confused by your order of operation, in example 1 do you mean:

    (x-2 - y-2)/(x-1 + y-1) ?
     
  6. Aug 19, 2003 #5

    Cod

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    That is correct. Sorry I couldn't make it look better. I'm not familiar with the coding for making squares and such.
     
  7. Aug 19, 2003 #6

    HallsofIvy

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    First rule: If there is any chance of ambiguity, use parentheses!


    The formula you give first: x^-2 - y^-2 / x^-1 + y^-1
    could be interpreted as x-2- (y-2/x-1)+ y-1 or as (x-2-y-2)/(x-1+ y-1).

    The first of the two would be technically correct but I suspect you mean the second.
    To simplify (x-2-y-2)/(x-1+ y-1), multiply both numerator and denominator by x2y2 (this is essentially the same as multiplying several fractions by the least common denominator).

    You get (y2- x2)/(xy2-x2y). Now factor and simplify.
     
  8. Aug 19, 2003 #7
    Not according to my calculations.


    Cod,
    Could you show what the problem looked like immediately after making the exponents positive?
    [edit]
    Cod,
    Scratch that. Better do it as HallsofIvy's showed (if you can figure out where the X2Y2 comes from, that is).

    [edit]
    HallsofIvy,
    Did you type in a '-' where a '+' was supposed to go?
     
    Last edited by a moderator: Aug 19, 2003
  9. Aug 20, 2003 #8

    HallsofIvy

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    Thanks, Boulderhead, I did slip an extra negative into that.


    It should be (y2- x2)/(xy2+x2y).

    I must have rocks in my head!
     
  10. Aug 20, 2003 #9
    You're welcome.

    Why, that's nothing at all. I’m running a regular sand and gravel business over on my end!
     
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