To solve the given question, we need to find the value of [tex]\( \left( \frac{f}{g} \right)(-7) \)[/tex], where [tex]\( f(x) = 5 - x \)[/tex] and [tex]\( g(x) = x^2 + 3x - 2 \)[/tex].
1. Evaluate [tex]\( f(-7) \)[/tex]:
Given [tex]\( f(x) = 5 - x \)[/tex],
[tex]\[
f(-7) = 5 - (-7) = 5 + 7 = 12
\][/tex]
2. Evaluate [tex]\( g(-7) \)[/tex]:
Given [tex]\( g(x) = x^2 + 3x - 2 \)[/tex],
[tex]\[
g(-7) = (-7)^2 + 3(-7) - 2 = 49 - 21 - 2 = 26
\][/tex]
3. Calculate [tex]\( \left( \frac{f}{g} \right)(-7) \)[/tex]:
[tex]\[
\left( \frac{f}{g} \right)(-7) = \frac{f(-7)}{g(-7)} = \frac{12}{26}
\][/tex]
Simplify [tex]\(\frac{12}{26}\)[/tex]:
[tex]\[
\frac{12}{26} = \frac{6}{13}
\][/tex]
So, [tex]\( \left( \frac{f}{g} \right)(-7) = 0.46153846153846156 \)[/tex].
Therefore, the step-by-step solution yields the following:
[tex]\[
\boxed{0.46153846153846156}
\][/tex]
