Here's a detailed, step-by-step solution to the problem:
Given the function [tex]\( f(x) = \frac{3 + x}{x - 3} \)[/tex], we want to find the expression for [tex]\( f(a + 2) \)[/tex].
1. Substitute [tex]\( a + 2 \)[/tex] into the function:
[tex]\[ f(a + 2) = \frac{3 + (a + 2)}{(a + 2) - 3} \][/tex]
2. Simplify the numerator:
[tex]\[ 3 + (a + 2) = 3 + a + 2 = a + 5 \][/tex]
3. Simplify the denominator:
[tex]\[ (a + 2) - 3 = a + 2 - 3 = a - 1 \][/tex]
4. Combine the simplified numerator and denominator:
[tex]\[ f(a + 2) = \frac{a + 5}{a - 1} \][/tex]
Thus, the expression for [tex]\( f(a + 2) \)[/tex] is [tex]\(\frac{a + 5}{a - 1}\)[/tex].
So, the correct answer is:
A. [tex]\(\frac{5 + a}{a - 1}\)[/tex]
