Question

F(x) = x ^ 2 - x - 6; g(x) = 2x ^ 2 + 5x + 2 Find: (f/g)(X)

Answer 1

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

Explanation:

Given

`f(x) =x^2 -x - 6`

`g(x) = 2x^2 + 5x + 2`

Required

`((f)/(g))(x)`

This is calculated as:

`((f)/(g))(x) = (f(x))/(g(x))`

So, we have:

`((f)/(g))(x) = (x^2 - x - 6)/(2x^2 + 5x + 2)`

Expand

`((f)/(g))(x) = (x^2 +2x - 3x - 6)/(2x^2 + 4x+x + 2)`

Factorize

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

Factor out x + 2

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

Cancel out x + 2

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