The given text is simply a fraction and does not constitute a complete question or task. Here is an example of a complete and meaningful mathematical question involving the fraction:

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Simplify the following fraction:

[tex]\frac{5}{2}[/tex]
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Or, if it's meant to be a standalone fraction representation, you can format it as:

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The fraction is:

[tex]\frac{5}{2}[/tex]
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Answer :

Sure, let's go through the steps to solve the equation [tex]\( 4(18 - 3k) = 9(k + 1) \)[/tex].

1. Distribute the constants:
- Distribute the 4 on the left side: [tex]\( 4(18) - 4(3k) = 72 - 12k \)[/tex].
- Distribute the 9 on the right side: [tex]\( 9(k) + 9(1) = 9k + 9 \)[/tex].

So, after distributing, we have:
[tex]\[ 72 - 12k = 9k + 9 \][/tex]

2. Move all terms involving [tex]\( k \)[/tex] to one side and constants to the other side:
- Add [tex]\( 12k \)[/tex] to both sides to move the [tex]\( k \)[/tex]-terms to one side:
[tex]\[ 72 = 9k + 12k + 9 \][/tex]
[tex]\[ 72 = 21k + 9 \][/tex]

- Subtract 9 from both sides to move the constants to the other side:
[tex]\[ 72 - 9 = 21k \][/tex]
[tex]\[ 63 = 21k \][/tex]

3. Solve for [tex]\( k \)[/tex]:
- Divide both sides by 21:
[tex]\[ \frac{63}{21} = k \][/tex]
[tex]\[ 3 = k \][/tex]

So, the solution to the equation [tex]\( 4(18 - 3k) = 9(k + 1) \)[/tex] is:
[tex]\[ k = 3 \][/tex]

This means the value of [tex]\( k \)[/tex] that satisfies the equation is [tex]\( \boxed{3} \)[/tex].