Final answer:
The given expression is simplified by multiplying the numerator by the reciprocal of the denominator, which results in the simplified single rational expression 1 / (2x^2). There seems to be an error in the provided options as none matches the correct answer. option d is the correct answer.
Step-by-step explanation:
The question asks to write the expression 1 over x cubed divided by 2 over x as a single rational expression. This can be solved by multiplying the first fraction by the reciprocal of the second fraction:
(1 / x^3) × (x / 2) = x / (2x^3)
Now, simplify by cancelling out an x from the numerator and denominator:
x / (2x^3) = 1 / (2x^2)
To write the given expression as a single rational expression, we need to divide the numerator 1/x³ by the denominator 2/x. When we divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, the expression can be written as:
(1/x³) / (2/x) = (1/x³) * (x/2)
Simplifying further, we get:
(1*x) / (x³*2) = x / (2x³) = 1/(2x²)
As a single rational expression, the answer is 1 / (2x^2), which matches none of the given options A) x² - 2 B) x² + 2 C) x - 2 D) x + 2. There might be a typographical error in the options provided.