1964 AHSME Problems/Problem 4
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Problem
The expression
![\[\frac{P+Q}{P-Q}-\frac{P-Q}{P+Q}\]](http://latex.artofproblemsolving.com/b/5/7/b57109c95c86c11d20d59d6813fcf623a616b884.png)
where 
and 
, is equivalent to:
Solution 1
Simplifying before substituting by obtaining a common denominator gives:
Substituting gives:
Solution 2
Substituting and then simplifying, noting that 
and 
, gives:
Solution 3
If it's true for all values of 
and 
, then it's true for a specific value of and . Letting 
and 
gives 
and 
. The fraction becomes:
Plugging in 
into the answer choices gives 
. Therefore, the answer is
See Also
| 1964 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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. 
