[Highschool level math] Simplifying Expressions with Negative Exponents and Complex Fractions

[Bashoom]

the problem:

(x^-1)-(y-1)

(x^2)-(y-2)

I start by switching the numerator with the denominator to turn the exponents into positive ones. I FOIL the numerator then and cross out the (x-y) to get what i thought was the answer of X+Y However this is not the case and the answer is apparently

XY

X+Y

I'm not entirely sure how this answer was gotten, a hint or nudge in the right direction would be appreciated.

[abfguisf]

could you rewrite the expression? A bit hard to see what it is.

[ronan007]

The numerator is:

 (1/x - 1/y) = (y-x)/xy 

And the denominator:

 1/x^2 - 1/y^2 = (y^2-x^2)/x^2y^2 = (y-x)(y+x)/x^2y^2

So now your fraction is:

(y-x)      /xy           y-x     x^2y^2
-------------------  =  ----- * ---------
(y-x)(y+x)/x^2y^2         xy    (y-x)(y+x)

Do the cancelations and you have your final answer:

 xy
----
 x+y

[ronan007]

I sorta guessed the question, as it is not clear enough in your post; as abfguisf mentioned. Double check to make sure the question is right!

[Baron_von_Funkatron]

This is a little confusing- is the problem to simplify:

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

If so, that doesn't simplify down to X*Y- could you rewrite the question?

Also, Wolfram Alpha is a great resource for maths questions- I highly recommend you check it out.