Understanding Negative Exponents in College Algebra

[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]

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!