2. What is the quotient represented by the expression \( \frac{3 x^{2}+3}{x^{2}+1} \) for all values of \( x \) where the expression is defined? A. 6 B. 3 C. -3 D. \( \frac{1}{3} \)

To determine the quotient represented by the expression \( \frac{3x^{2} + 3}{x^{2} + 1} \) for all values of \( x \) where the expression is defined, let's simplify the expression: \[ \frac{3x^{2} + 3}{x^{2} + 1} = \frac{3(x^{2} + 1)}{x^{2} + 1} \] Here, \( x^{2} + 1 \) is present in both the numerator and the denominator, and since \( x^{2} + 1 \) is never zero (for all real \( x \)), we can cancel it out: \[ \frac{3(x^{2} + 1)}{x^{2} + 1} = 3 \] Thus, the expression simplifies to the constant value **3** for all real values of \( x \). **Answer:** B. 3