# College Algebra Question

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.

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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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Example 1: x^-2 - y^-2 / x^-1 + y^-1
So the correct answer would be:

2y - 2x / y + x ??

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

(x-2 - y-2)/(x-1 + y-1) ?

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
Homework Helper
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.

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?

Cod,
Scratch that. Better do it as HallsofIvy's showed (if you can figure out where the X2Y2 comes from, that is).

HallsofIvy,
Did you type in a '-' where a '+' was supposed to go?

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

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

I must have rocks in my head!