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College Algebra Question

  • Thread starter Cod
  • Start date
  • #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.
 

Answers and Replies

  • #2
BoulderHead
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.
 
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  • #3
Cod
324
4
Example 1: x^-2 - y^-2 / x^-1 + y^-1
So the correct answer would be:

2y - 2x / y + x ??
 
  • #4
jcsd
Science Advisor
Gold Member
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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) ?
 
  • #5
Cod
324
4
Originally posted by jcsd
I'm a bit confused by your order of operation, in example 1 do you mean:

(x-2 - y-2)/(x-1 + y-1) ?
That is correct. Sorry I couldn't make it look better. I'm not familiar with the coding for making squares and such.
 
  • #6
HallsofIvy
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Homework Helper
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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.
 
  • #7
BoulderHead
So the correct answer would be:

2y - 2x / y + x ??
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?
 
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  • #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!
 
  • #9
BoulderHead
You're welcome.

Originally posted by HallsofIvy
… I must have rocks in my head!
Why, that's nothing at all. I’m running a regular sand and gravel business over on my end!
 

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