Bunuel wrote:
If \(2x \neq y\) and \(5x \neq 4y\), what is the value of \(\frac{\frac{5x-4y}{2x-y}}{\frac{3y}{y-2x} + 5}\) ?
A. \(\frac{1}{2}\)
B. \(\frac{3}{2}\)
C. \(\frac{5}{2}\)
D. \(\frac{7}{2}\)
E. \(\frac{9}{2}\)
\(\frac{\frac{5x-4y}{2x-y}}{\frac{3y}{y-2x} + 5}\)
=\(\frac{\frac{5x-4y}{2x-y}}{\frac{8y-10x}{y-2x}}\)
=\(\frac{\frac{5x-4y}{2x-y}}{\frac{10x-8y}{2x-y}}\)
=\(\frac{5x-4y}{10x-8y}\)
=\(\frac{1}{2}\)
IMO A
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