Find the domain of (f(x)=\frac{x+1}{x^2-9}).

Correct answer: (\mathbb{R}-{-3,3})

The direct answer is option A: the domain is all real numbers except −3 and 3, written ℝ\{−3,3}. A rational function is defined wherever its denominator is not zero. Here the denominator is x²−9. Set it equal to zero: x²−9=0, so x²=9 and x=3 or x=−3. These two values must be excluded. The numerator x+1 causes no restriction because it is allowed to be zero; a zero numerator simply makes the function value zero, provided the denominator is nonzero. Option A correctly removes both forbidden values. Option B removes only 3 and wrongly allows −3, where the denominator is zero. Option C removes only −3 and wrongly allows 3. Option D lists only the excluded values instead of all permitted real values. Every other real number is allowed, including x=−1, where the numerator is zero and the denominator is −8. Memory cue: for a fraction, solve denominator=0 and delete those values only; never delete values merely because the numerator is zero.