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Difference between revisions of "1955 AHSME Problems/Problem 4"

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==Solution==
 
==Solution==
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From the equality, <math>\frac{1}{x-1}=\frac{2}{x-2}</math>, we get  <math>{(x-1)}\times2={(x-2)}\times1</math>.
  
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From the equality, <math>\frac{1}{x-1}=\frac{2}{x-2}</math>, we get  <math>{(x-1)}*2={(x-2)}*1</math>.
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Solving this, we get, <math>{2x-2}={x-2}</math>.
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Thus, the answer is <math>\fbox{{\bf(E)} \text{only} x = 0}</math>.
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Solution by awesomechoco
  
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Solving this, we get, <math>{2x-2}={x-2}</math>.
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== See Also ==
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{{AHSME box|year=1955|num-b=3|num-a=5}}
  
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Thus, {only}x=0<math> can satisfy the equation, {(E)}</math>
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{{MAA Notice}}

Latest revision as of 22:14, 9 July 2018

Problem

The equality $\frac{1}{x-1}=\frac{2}{x-2}$ is satisfied by:

$\textbf{(A)}\ \text{no real values of }x\qquad\textbf{(B)}\ \text{either }x=1\text{ or }x=2\qquad\textbf{(C)}\ \text{only }x=1\\ \textbf{(D)}\ \text{only }x=2\qquad\textbf{(E)}\ \text{only }x=0$

Solution

From the equality, $\frac{1}{x-1}=\frac{2}{x-2}$, we get ${(x-1)}\times2={(x-2)}\times1$.

Solving this, we get, ${2x-2}={x-2}$.

Thus, the answer is $\fbox{{\bf(E)} \text{only} x = 0}$.

Solution by awesomechoco

See Also

1955 AHSME (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
All AHSME Problems and Solutions


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