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1954 AMC 12 Question 2

AMC12 · 1954 AMC 12

Question 2

The equation $$
\begin{aligned} \frac{2x^2}{x-1}-\frac{2x+7}{3} &{}+\frac{4-6x}{x-1}\\ &{}+1=0 \end{aligned}
$$ can be transformed by eliminating fractions to the equation $x^2-5x+4=0.$ The roots of the latter equation are $4$ and $1.$ Then the roots of the first equation are:
  1. $4$ and $1$
  2. only $1$
  3. only $4$
  4. neither $4$ nor $1$
  5. $4$ and some other root