Final answer:
None of the provided options is clearly equal to the indicated rational expression when x is not equal to 1 or -1, as there is insufficient context to determine their equivalence.
Step-by-step explanation:
The question asks which of the given options is equal to a certain rational expression when x is not equal to 1 or -1. To determine this, we need to analyze the provided options and look for equivalencies based on algebraic rules.
Option 1: (x + 1) / (x - 1). This is a rational expression but does not simplify to any other given options.
Option 2: 5. This is a constant value, not equivalent to a variable expression unless under specific conditions not stated here.
Option 3: 5(x - 1) / (x + 1)(x - 1). Once we simplify this expression by canceling out the common factors in the numerator and the denominator, we are left with 5/(x+1), which is again not equivalent to any other given options.
Option 4: 5 / (x - 1). This expression does not simplify to match the algebraic equivalence of any of the other options.
None of the options are equal to the same rational expression unless more context is provided. Thus, without additional information, none of the given options can be determined as equivalent to the rational expression in question when x ≠ 1 or -1.