Difference between revisions of "1992 AHSME Problems/Problem 6"
(Created page with "== Problem == If <math>x>y>0</math> , then <math>\frac{x^y y^x}{y^y x^x}=</math> <math>\text{(A) } (x-y)^{y/x}\quad \text{(B) } \left(\frac{x}{y}\right)^{x-y}\quad \text{(C) }...") |
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== Solution == | == Solution == | ||
− | <math>\fbox{D}</math> | + | We see that this fraction can easily be factored as <math>\frac{x^y}{y^y}\times\frac{y^x}{x^x}</math>. Since <math>\frac{y^x}{x^x}=\frac{x^{-x}}{y^{-x}}</math>, this fraction is equivalent to <math>(\frac{x}{y})^y\times(\frac{x}{y})^{-x}=(\frac{x}{y})^{y-x}</math>, which corresponds to answer choice <math>\fbox{D}</math>. |
== See also == | == See also == |
Revision as of 22:49, 4 October 2016
Problem
If , then
Solution
We see that this fraction can easily be factored as . Since
, this fraction is equivalent to
, which corresponds to answer choice
.
See also
1992 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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All AHSME Problems and Solutions |
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