MathDB
Eliminating Fractions

Source:

February 6, 2009

Problem Statement

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 and 1 1. Then the roots of the first equation are: <spanclass=latexbold>(A)</span> 4 and 1<spanclass=latexbold>(B)</span> only 1<spanclass=latexbold>(C)</span> only 4<spanclass=latexbold>(D)</span> neither 4 nor 1<spanclass=latexbold>(E)</span> 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}