If f(x)=(x+2)/(x−2) and g(x)=(x−2)/(x+2), what is the simplified form of (f+g)(x)?

Correct answer: (2x²+8)/(x²−4), x≠±2

To add the rational functions, use the common denominator (x−2)(x+2)=x²−4. Thus (f+g)(x)=(x+2)/(x−2)+(x−2)/(x+2)=[(x+2)²+(x−2)²]/(x²−4). Expanding the numerator gives (x²+4x+4)+(x²−4x+4)=2x²+8, because the middle terms cancel. Therefore (f+g)(x)=(2x²+8)/(x²−4). The original denominators require x−2≠0 and x+2≠0, so x≠2 and x≠−2, written x≠±2. Hence option A is correct. Option B has an incorrect sign in the constant term, option C loses the squared terms, and option D omits the factor 2. No cancellation removes the original domain restrictions.