To solve this problem, we need to follow the verbal description step-by-step and translate it into a mathematical expression. Let's break it down:
1. Identify the sum described: We are given "the sum of 7 times [tex]$x$[/tex] and 3".
- Mathematically, this is written as [tex]\(7x + 3\)[/tex].
2. Square the sum: The next part of the description asks us to take the square of the sum [tex]\(7x + 3\)[/tex].
- This becomes [tex]\((7x + 3)^2\)[/tex].
3. Identify the difference described: We then consider "the difference of [tex]$x$[/tex] and 1".
- Mathematically, this is written as [tex]\(x - 1\)[/tex].
4. Multiply the difference by 4: The description asks for "4 times the difference".
- So, we multiply [tex]\((x - 1)\)[/tex] by 4, which gives [tex]\(4(x - 1)\)[/tex].
5. Form the fraction: Finally, we need to divide the squared sum by 4 times the difference.
- This fraction is [tex]\(\frac{(7x + 3)^2}{4(x - 1)}\)[/tex].
Given these steps, the expression that represents the verbal description is:
[tex]\[ \frac{(7x + 3)^2}{4(x - 1)} \][/tex]
Thus, the correct answer is:
D. [tex]\(\frac{(7x+3)^2}{4(x-1)}\)[/tex]
