Question

Which of the following represents the expression 4x / 40x - 1 ÷ 4 / x² - 41? a) 4x² - 164x / 160x³ - 4x b) 4x² - 164x / 40x³ - x c) 4x² - 160x / 160x³ - 4x d) 4x² - 160x / 40x³ - x

Answer 1

The expression 4x / 40x - 1 ÷ 4 / x² - 41 can be simplified by applying the order of operations. The simplified representation is c) 4x² - 160x / 160x³ - 4x.

Step-by-step explanation:

The expression 4x / 40x - 1 ÷ 4 / x² - 41 can be simplified by applying the order of operations (PEMDAS/BODMAS). Let's break it down step by step:

1. First, simplify 4x / 40x - 1. This can be rewritten as 4x / (40x - 1).
2. Next, simplify 4 / x² - 41. This can be rewritten as 4 / (x² - 41).
3. The expression can now be written as (4x / (40x - 1)) ÷ (4 / (x² - 41)).
4. To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. So, (4x / (40x - 1)) ÷ (4 / (x² - 41)) becomes (4x / (40x - 1)) * ((x² - 41) / 4).
5. Simplifying further, we get (4x * (x² - 41)) / (4 * (40x - 1)).
6. Further simplifying, we have (4x³ - 164x) / (160x³ - 4x).

Therefore, the expression 4x / 40x - 1 ÷ 4 / x² - 41 is represented by the option: c) 4x² - 160x / 160x³ - 4x.