Sure, let's simplify the given fraction step by step.
We start with the fraction:
[tex]\[
\frac{12k + 54}{12k}
\][/tex]
First, we'll split the fraction into two separate terms:
[tex]\[
\frac{12k}{12k} + \frac{54}{12k}
\][/tex]
Next, we'll simplify each term individually.
The first term:
[tex]\[
\frac{12k}{12k} = 1
\][/tex]
The second term:
[tex]\[
\frac{54}{12k} = \frac{54}{12} \cdot \frac{1}{k} = \frac{9}{2k}
\][/tex]
Now, we combine the simplified terms:
[tex]\[
1 + \frac{9}{2k}
\][/tex]
Looking at the options provided:
A) [tex]\(\frac{5k-3}{2k}\)[/tex]
B) [tex]\(\frac{6}{7k-1}\)[/tex]
C) [tex]\(\frac{9}{3k+10}\)[/tex]
D) [tex]\(\frac{2k+9}{2k}\)[/tex]
We can see that option D matches our simplified form:
[tex]\[
1 + \frac{9}{2k} = \frac{2k}{2k} + \frac{9}{2k} = \frac{2k+9}{2k}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{D}
\][/tex]
