Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

Hi!
I have a problem that I got wrong on an exam that I literally have no idea how to solve because
the teacher just marked it wrong but never gave the right answer. It looks like this:

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

can someone please show me step by step how to do this so I can learn for my final how to do it?

Thanks!
kristen_nicsxo

Posts: 2
Joined: Thu Dec 13, 2012 1:29 am

the line that looks like this ---------- is supposed to be a division line. The problem is a fraction!
kristen_nicsxo

Posts: 2
Joined: Thu Dec 13, 2012 1:29 am

There don't appear to be any instructions. Were you maybe supposed to "simplify", maybe to get all positive powers? They show how to do that sort of thing here. You'd start with:

$\frac{x^{-1}\, -\, y^{-1}}{x^{-2}\, -\, y^{-2}}$

Then you'd turn it all into positive powers:

$\frac{\frac{1}{x}\, -\, \frac{1}{y}}{\frac{1}{x^2}\, -\, \frac{1}{y^2}}$

Then you'd do common denominators:

$\frac{\frac{y}{xy}\, -\, \frac{x}{xy}}{\frac{y^2}{x^2y^2}\, -\, \frac{x^2}{x^2y^2}}$

Etc, etc, and so forth.

maggiemagnet

Posts: 288
Joined: Mon Dec 08, 2008 12:32 am

More efficient to multiply numerator and denominator by the lowest common denominator, $\frac{x^2y^2}{x^2y^2}$.