Answer:
[tex]-\frac{104}{41}[/tex]
Step-by-step explanation:
[tex]\frac{f(x)}{g(x)}=\frac{3-2x}{\frac{1}{x} +5}[/tex]
To make this easier to deal with, we can plug in 8 first:
- [tex]\frac{f(8)}{g(8)}=\frac{3-2(8)}{\frac{1}{(8)}+5 }[/tex]
- Then we can simplify the terms to get [tex]\frac{3-16}{\frac{1}{8} +5}=\frac{-13}{\frac{1}{8} +5}[/tex]
- The denominator of this fraction needs to have its own common denominator. To do so, we can multiply the 5 by [tex]\frac{8}{8}[/tex] to give us: [tex]\frac{1}{8}+\frac{40}{8}[/tex]
- We can then simplify this to [tex]\frac{41}{8}[/tex]
- Now putting this back into our original fraction we have: [tex]\frac{-13}{\frac{41}{8} }[/tex]
- This is also equivalent to [tex]\frac{(\frac{-13}{1} )}{(\frac{41}{8} )}[/tex] which means we need to take the whole denominator of the fraction and flip it and multiply it by the numerator to get: [tex]\frac{-13}{1}*\frac{8}{41}[/tex]
- This then simplifies to [tex]\frac{-104}{41}[/tex]
