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Omni-MATH / Two positive rational numbers x and y, when written in lowest terms, have the property that the sum of their numerators is 9 and the sum of their denominators is 10 . What is the l…

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Two positive rational numbers xx and yy, when written in lowest terms, have the property that the sum of their numerators is 9 and the sum of their denominators is 10 . What is the largest possible value of x+yx+y ?
Plain-text mathematical notation (without MathML)
Two positive rational numbers x and y, when written in lowest terms, have the property that the sum of their numerators is 9 and the sum of their denominators is 10 . What is the largest possible value of x+y ?
Original LaTeX notation
Two positive rational numbers $x$ and $y$, when written in lowest terms, have the property that the sum of their numerators is 9 and the sum of their denominators is 10 . What is the largest possible value of $x+y$ ?

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