If f(x)=1/(x+1) and g(x)=1/(x−1), what is the simplified form of (f+g)(x)?

Correct answer: 2x/(x²−1), x ≠ ±1

The governing concept is addition of rational functions by using a common denominator while retaining domain restrictions. Start with (f+g)(x)=1/(x+1)+1/(x−1). The common denominator is (x+1)(x−1)=x²−1. Combining the numerators gives (x−1)+(x+1)=2x, so the sum becomes 2x/(x²−1). The original denominators show that x cannot be −1 or 1; these exclusions remain even if a later algebraic expression appears simplified. Therefore option A is correct. Option B omits x from the numerator, option C omits the factor 2, and option D uses the false identity (x+1)(x−1)=x²+1 and incorrectly allows all real x.