2014 AIME I Problems/Problem 14: Difference between revisions
| Line 9: | Line 9: | ||
== Solution == | == Solution == | ||
The first step is to notice that the 4 on the right hand side can simplify the terms on the left hand side. If we distribute 1 to <math>3/x-3</math>, then the fraction becomes of the form <math>(x/x - 3)</math>. A similar cancellation happens with the other four terms. | The first step is to notice that the 4 on the right hand side can simplify the terms on the left hand side. If we distribute 1 to <math>3/x-3</math>, then the fraction becomes of the form <math>(x/x - 3)</math>. A similar cancellation happens with the other four terms. | ||
<math>/ /</math> | |||
== See also == | == See also == | ||
{{AIME box|year=2014|n=I|num-b=13|num-a=15}} | {{AIME box|year=2014|n=I|num-b=13|num-a=15}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 19:34, 14 March 2014
Problem 14
Let 
be the largest real solution to the equation
There are positive integers 
, 
, and 
such that 
. Find 
.
Solution
The first step is to notice that the 4 on the right hand side can simplify the terms on the left hand side. If we distribute 1 to 
, then the fraction becomes of the form 
. A similar cancellation happens with the other four terms.
See also
| 2014 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America. 
