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Difference between revisions of "1967 AHSME Problems/Problem 10"

(Created page with "== Problem == If <math>\frac{a}{10^x-1}+\frac{b}{10^x+2}=\frac{2 \cdot 10^x+3}{(10^x-1)(10^x+2)}</math> is an identity for positive rational values of <math>x</math>, then the va...")
 
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== Solution ==
 
== Solution ==
 
<math>\fbox{A}</math>
 
<math>\fbox{A}</math>
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== See also ==
 
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{{AHSME box|year=1967|num-b=9|num-a=11}} 
 
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[[Category:Introductory Algebra Problems]]
 
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{{MAA Notice}}
 

Revision as of 19:50, 10 February 2016

Problem

If $\frac{a}{10^x-1}+\frac{b}{10^x+2}=\frac{2 \cdot 10^x+3}{(10^x-1)(10^x+2)}$ is an identity for positive rational values of $x$, then the value of $a-b$ is:

$\textbf{(A)}\ \frac{4}{3} \qquad \textbf{(B)}\ \frac{5}{3} \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ \frac{11}{4} \qquad \textbf{(E)}\ 3$

Solution

$\fbox{A}$

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