What is the domain of f(x) = (x − 1)/(x² + 2x − 3)?

Correct answer: ℝ \ {1, −3}

A rational function is defined for every real x except those values that make its denominator zero. Factor the denominator: x² + 2x − 3 = (x + 3)(x − 1). Hence the denominator is zero at x = −3 and x = 1. These two values must be excluded, while every other real number is allowed. Therefore the domain is ℝ \ {−3, 1}, which is the same set as ℝ \ {1, −3}; option A is correct. The numerator being zero at x = 1 does not cancel the original restriction, because the original denominator is also zero there. Option B contains the wrong excluded values, option C omits −3, and option D wrongly removes intervals instead of only two points. The governing concept is finding and excluding zeros of the original denominator.