Question

Which of the following is the product of the rational expression shown below?

5/2x-1 × 5/x

A 25/2x² - x
B 10/2x-1
C 25/2x² - x + 5
D 25/2x² - x - 5

Answer 1

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.