Question

Given f(x) = 4x+ 6x and g(x) = 2x^2 + 13x +15, find (f/g) (x). Show your work

Answer 1

`(2x)/(x+5)`

Explanation:

We are given the following two functions and we are to find
`\frac {f} {g} (x)`:

`f(x) = 4x + 6x`

`g(x) = 2x^2 + 13x +15`

Factorizing both the functions before solving them further.

`f(x) = 4x + 6x = 2x (2x+3)`

`g(x) = 2x^2 + 13x + 15 = x^2+3x+10x+15 = (x+5) (2x+3)`

Finding
`\frac {f} {g} (x)`:

`\frac {f} {g} (x)`
`=(2x(2x+3))/((x+5)(2x+3)) = (2x)/(x+5)`