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].
