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College Algebra Question

  1. Aug 18, 2003 #1


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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


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    So the correct answer would be:

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


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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


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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


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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.

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

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


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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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