Final answer:
The relationship between the ratios (a)/(x-1) and (a)/(x) is such that (a)/(x-1) is always greater than or equal to (a)/(x) for positive natural numbers, assuming x is greater than a. By comparing different values for a and x, it's observed that as x increases, the value of (a)/(x) decreases.
Step-by-step explanation:
The question involves investigating the relationship between two ratios: (a)/(x-1) and (a)/(x), given that a is greater than 0 and x is greater than 1. To explore this relationship, we can select different positive natural numbers for a and x and then compare the two ratios.
Let's take a = 2 and x = 3 as an example. The first ratio would be (2)/(3-1) = 2/2 = 1, and the second would be (2)/(3) which is approximately 0.67. Now let's take a = 5 and x = 6. The first ratio is (5)/(6-1) = 5/5 = 1, and the second is (5)/(6) which is approximately 0.83.
From these examples, we can observe that the ratio (a)/(x-1) is always equal to 1 when x = a + 1, while the ratio (a)/(x) is always less than 1 if x is greater than a. As x continues to increase, the value of (a)/(x) decreases. This establishes that for positive natural numbers, (a)/(x-1) is always greater than or equal to (a)/(x) assuming x> a.