Final answer:
The product of the rational expressions 5/(2x-1) and 5/x is 25/2x² - x, which corresponds to option A. This is calculated by multiplying the numerators together and the denominators together.
Step-by-step explanation:
The question asks about finding the product of two rational expressions, specifically the product of 5/(2x-1) and 5/x. To multiply two fractions, you multiply the numerators together and the denominators together. In this case:
- Multiply the numerators: 5 × 5 = 25.
- Multiply the denominators: (2x-1) × x = 2x² - x.
Therefore, the product of the given rational expressions is 25/2x² - x, which matches option A. When multiplying factors with the same base, you can add the exponents, for example, 5¹ × 5¹ = 5. Similarly, when multiplying algebraic expressions, you apply the distributive property to find the product of the two denominators.