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National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1954 AMC 12/AHSME
2
2
Part of
1954 AMC 12/AHSME
Problems
(1)
Eliminating Fractions
Source:
2/6/2009
The equation \frac{2x^2}{x\minus{}1}\minus{}\frac{2x\plus{}7}{3}\plus{}\frac{4\minus{}6x}{x\minus{}1}\plus{}1\equal{}0 can be transformed by eliminating fractions to the equation x^2\minus{}5x\plus{}4\equal{}0. The roots of the latter equation are
4
4
4
and
1
1
1
. Then the roots of the first equation are:
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A
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4
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1
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B
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only
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C
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only
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D
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neither 4 nor 1
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E
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4 and some other root
<span class='latex-bold'>(A)</span>\ 4 \text{ and }1 \qquad <span class='latex-bold'>(B)</span>\ \text{only }1 \qquad <span class='latex-bold'>(C)</span>\ \text{only }4 \qquad <span class='latex-bold'>(D)</span>\ \text{neither 4 nor 1} \qquad <span class='latex-bold'>(E)</span>\ \text{4 and some other root}
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4
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only
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only
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D
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neither 4 nor 1
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E
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4 and some other root