1967 AHSME Problems/Problem 2
Problem
An equivalent of the expression
, 
,
is:
Solution
![\[\left(\frac{x^2+1}{x}\right)\left(\frac{y^2+1}{y}\right)+\left(\frac{x^2-1}{y}\right)\left(\frac{y^2-1}{x}\right)\]](http://latex.artofproblemsolving.com/a/1/b/a1b4279ca397d69d7acef9577c40a8bb5686a49b.png)
![\[\frac{(x^2+1)(y^2+1)}{xy} + \frac{(x^2-1)(y^2-1)}{xy}\]](http://latex.artofproblemsolving.com/8/6/7/867a2ec89a5cd57d9f19a5a16f15c73a35cd2e5e.png)
![\[\frac{(x^2y^2+x^2+y^2+1) + (x^2y^2-x^2-y^2+1)}{xy}\]](http://latex.artofproblemsolving.com/7/1/1/7112a42f609bd7c20b063d681bd2dfc3b3c4d15a.png)
![\[\frac{x^2y^2+x^2+y^2+1 + x^2y^2-x^2-y^2+1}{xy}\]](http://latex.artofproblemsolving.com/4/f/d/4fd946c9695f025b8d6f36f3d68b7441be6f36c3.png)
![\[\frac{2x^2y^2+2}{xy}\]](http://latex.artofproblemsolving.com/5/1/f/51f55750a9b528886e3ac3c562a4be28def0b33f.png)
![\[\frac{2x^2y^2}{xy} + \frac{2}{xy}\]](http://latex.artofproblemsolving.com/0/e/f/0efca0fb726b28157242c21b8aac1b73c207ef3a.png)
![\[\frac{2xy * xy}{xy} + \frac{2}{xy}\]](http://latex.artofproblemsolving.com/4/3/8/438284aa67a3a3f2562df57491abc44d859e4480.png)
![\[2xy + \frac{2}{xy}\]](http://latex.artofproblemsolving.com/d/0/3/d0392a6dace7686540219240f99918b1f0d9dfe1.png)
The answer is 
See Also
| 1967 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
