College Algebra Question...

[Cod]

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.

[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.

[Cod]

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

So the correct answer would be:

2y - 2x / y + x ??

[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) ?

[Cod]

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.

[HallsofIvy]

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.

[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?

[HallsofIvy]

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


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

I must have rocks in my head!

[BoulderHead]

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! [:D]