Final answer:
The domain is all real numbers except x = -1 and x = 1, and to solve the inequality, we must find the common denominator, create a quadratic inequality from it, solve for zero, and then test intervals around those solutions.
Step-by-step explanation:
The question asks us to find the domain and solve the inequality for the expression (2/(x+1)) ≥ (3/(x-1)). First, let's address the domain. The domain of a function includes all the values of x for which the function is defined. In this case, the function will be undefined when x + 1 = 0 and when x - 1 = 0. Therefore, x cannot be -1 or 1. Our domain is all real numbers except x = -1 and x = 1.
Now, to solve the inequality, we need to combine the two fractions and find the common denominator, which in this case is (x+1)(x-1). After working through this step, we will get a quadratic inequality that we have to solve for x. We need to find the critical points where the inequality is equal to zero and test intervals around those critical points to see where the inequality is true. The correct answer will be a range of x values for which the inequality holds true.