To analyze the situation, let's consider what it means for the expressions \( c/d \) and \( \frac{ad + bc}{bd} \) to be rational numbers.
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\( c/d \) being a rational number means that both \( c \) and \( d \) are either integers or both are rational numbers (i.e., can be expressed in the form of a fraction).
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\( \frac{ad + bc}{bd} \) being rational implies that \( ad + bc \) is a rational number and \( bd \) is a rational number (since \( bd \) is in the denominator).
Now, let's consider the fraction \( a/b \).
Since \( c/d \) is rational, this does not give us any direct information about whether \( a/b \) is rational or irrational.
Now, consider \( \frac{ad + bc}{bd} \):
- If we write \( ad + bc = a(d) + b(c) \), since \( b \) and \( d \) are rational numbers (if we assume \( a \) is rational, then \( a = m/n \) for integers \( m, n \)), and similarly for \( c \), we find that both terms \( ad \) and \( bc \) would still retain their qualification as rational numbers (because a product or sum of rational numbers is rational).
Now, without loss of generality, if \( a/b \) was irrational (Option 2), then \( ad \) (since \( d \) is rational) would likely also influence \( ad + bc \) into an irrational number, contradicting the statement that it is rational.
Thus, the only way for both \( c/d \) and \( \frac{ad + bc}{bd} \) to remain rational is if \( a/b \) is also rational.
Therefore, the correct answer is: 1 (Option 1: \( a/b \) is rational).