To solve for [tex]\(\left(\frac{r}{s}\right)(6)\)[/tex], we have two functions, [tex]\(r(x) = 3x - 1\)[/tex] and [tex]\(s(x) = 2x + 1\)[/tex]. We need to find the values of [tex]\(r(6)\)[/tex] and [tex]\(s(6)\)[/tex] and then compute the expression [tex]\(\frac{r(6)}{s(6)}\)[/tex].
First, evaluate [tex]\(r(6)\)[/tex]:
[tex]\[ r(6) = 3(6) - 1 = 18 - 1 = 17 \][/tex]
Next, evaluate [tex]\(s(6)\)[/tex]:
[tex]\[ s(6) = 2(6) + 1 = 12 + 1 = 13 \][/tex]
Now, compute [tex]\(\left(\frac{r}{s}\right)(6)\)[/tex]:
[tex]\[ \left(\frac{r}{s}\right)(6) = \frac{r(6)}{s(6)} = \frac{17}{13} \][/tex]
Therefore, the expression equivalent to [tex]\(\left(\frac{r}{s}\right)(6)\)[/tex] is:
[tex]\[ \frac{3(6) - 1}{2(6) + 1} \][/tex]
This matches the first option:
[tex]\[ \frac{3(6) - 1}{2(6) + 1} \][/tex]
Which simplifies to:
[tex]\[ \frac{17}{13} \][/tex]
So the correct option is:
[tex]\[ \frac{3(6)-1}{2(6)+1} \][/tex]
