Question

If f(x)=3-2xand g(x)= 1/x+5, what is the value of f/g (8)?

Answer 1

`-(104)/(41)`

Explanation:

`(f(x))/(g(x))=(3-2x)/((1)/(x) +5)`

To make this easier to deal with, we can plug in 8 first:

• 
  `(f(8))/(g(8))=(3-2(8))/((1)/((8))+5 )`
• Then we can simplify the terms to get
  `(3-16)/((1)/(8) +5)=(-13)/((1)/(8) +5)`
• The denominator of this fraction needs to have its own common denominator. To do so, we can multiply the 5 by
  `(8)/(8)` to give us:
  `(1)/(8)+(40)/(8)`
• We can then simplify this to
  `(41)/(8)`
• Now putting this back into our original fraction we have:
  `(-13)/((41)/(8) )`
• This is also equivalent to
  `(((-13)/(1) ))/(((41)/(8) ))` which means we need to take the whole denominator of the fraction and flip it and multiply it by the numerator to get:
  `(-13)/(1)*(8)/(41)`
• This then simplifies to
  `(-104)/(41)`