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The question asks about the difference between two rational expressions:

\[
\frac{a}{b} - \frac{c}{d}
\]

where \(a\), \(b\), \(c\), and \(d\) are elements of a set of polynomials \(P\), and \(b\) and \(d\) are non-zero polynomials.

### Solution:
The expression \(\frac{a}{b} - \frac{c}{d}\) can be rewritten with a common denominator:

\[
\frac{a}{b} - \frac{c}{d} = \frac{ad}{bd} - \frac{bc}{bd} = \frac{ad - bc}{bd}
\]

Since \(a\), \(b\), \(c\), and \(d\) are polynomials, the numerator \(ad - bc\) is a polynomial, and the denominator \(bd\) is also a polynomial (since both \(b\) and \(d\) are non-zero polynomials).

This means the result is a *rational expression*, as it is the ratio of two polynomials.

### Correct Answer:
- **The difference is a rational expression.**

Would you like further details or have any other questions? 

Here are 5 related questions to explore further:

1. What is the difference between a rational expression and a rational number?
2. How do you simplify differences of rational expressions?
3. Can a rational expression ever be an integer?
4. Why do we need to find a common denominator when subtracting rational expressions?
5. What properties of polynomials are preserved when forming rational expressions?

**Tip:** Always check if the denominator is non-zero when dealing with rational expressions to avoid undefined expressions.

Let P be the set of polynomials. Let a, b, c, and d be elements of P such that b and d are non-zero elements in P. Which statement about this difference is true? (a/b - c/d).

Explore how to subtract two rational expressions involving polynomials in the form a/b - c/d. This solution walks through using a common denominator to express the difference as a single rational expression. Suitable for high school algebra students.

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