Answer :

To solve the given expression:
[tex]\[ \frac{15 + 5 \times 3}{3^2 + 6} \][/tex]

we need to follow a step-by-step approach to evaluate both the numerator and the denominator before performing the division.

Step 1: Evaluate the numerator
The numerator of the expression is:
[tex]\[ 15 + 5 \times 3 \][/tex]

First, we perform the multiplication:
[tex]\[ 5 \times 3 = 15 \][/tex]

Next, we add this result to 15:
[tex]\[ 15 + 15 = 30 \][/tex]

So, the numerator evaluates to 30.

Step 2: Evaluate the denominator
The denominator of the expression is:
[tex]\[ 3^2 + 6 \][/tex]

First, we calculate the exponent:
[tex]\[ 3^2 = 9 \][/tex]

Next, we add 6 to this result:
[tex]\[ 9 + 6 = 15 \][/tex]

So, the denominator evaluates to 15.

Step 3: Divide the numerator by the denominator
Now we divide the evaluated numerator by the evaluated denominator:
[tex]\[ \frac{30}{15} = 2.0 \][/tex]

So, the value of the expression is:
[tex]\[ 2.0 \][/tex]

Therefore, the correct answer is [tex]\( \boxed{2} \)[/tex].