It looks like there may have been a small typo in your question regarding the second fraction. I will assume you meant to input a fraction, but since it's incomplete, I'll show you how to find the product of \( \frac{5}{6} \) and a fraction \( \frac{11}{x} \) for some \( x \).
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Finding the product: The product of \( \frac{5}{6} \) and \( \frac{11}{x} \) is given by:
\[ \frac{5}{6} \times \frac{11}{x} = \frac{5 \times 11}{6 \times x} = \frac{55}{6x} \]
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Simplifying the result: The fraction \( \frac{55}{6x} \) is in simplest form as long as \( x \) does not have any common factors with 55 or 6. If \( x \) is any number other than 1 or a common factor, \( \frac{55}{6x} \) does not further simplify.
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Determining rationality: The result \( \frac{55}{6x} \) is a rational number as long as \( x \) is a non-zero integer. This is because any fraction (where the numerator and denominator are integers) is considered a rational number.
If you can provide me with the exact second fraction intended, I can give you a precise answer regarding the product and its simplest form.