To find the missing denominator in the expression \( \frac{3}{5} - \frac{1}{?} \), we need to determine a value that makes the subtraction meaningful.
Let's denote the missing denominator as \( x \). The key is to get a common denominator in order to perform the subtraction. The common denominator for \( \frac{3}{5} \) and \( \frac{1}{x} \) would be \( 5x \).
Rewriting both fractions with the common denominator:
\[ \frac{3}{5} = \frac{3x}{5x} \]
\[ \frac{1}{x} = \frac{5}{5x} \]
Now, the subtraction becomes:
\[ \frac{3x}{5x} - \frac{5}{5x} = \frac{3x - 5}{5x} \]
To make \( \frac{1}{x} \) a valid fraction such that the subtraction can be executed, the term \( 1/x \) must not result in a negative value when \( \frac{3}{5} \) is subtracted from it.
Since we are looking for the simplest fraction that leads to a meaningful subtraction, let’s approach it via setting \( \frac{3}{5} - \frac{1}{2} \):
- Here, apply the same common denominator of 10:
\[ \frac{3}{5} = \frac{6}{10} \]
\[ \frac{1}{2} = \frac{5}{10} \]
So:
\[ \frac{3}{5} - \frac{1}{2} = \frac{6}{10} - \frac{5}{10} = \frac{1}{10} \]
In that particular case, your \( x \) can be \( 2 \).
However, the problem demands deriving from \( \frac{1}{?} \) that directly corresponds. This means \( ? = 2 \) because:
\[ \frac{3}{5} - \frac{1}{2} = \text{subtraction resolves correctly as shown above, making denominator the part of original fraction } \]
Thus the missing denominator \( ?\) we determine is \( \mathbf{2} \).
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