Question

. Given 2f x x x 4 6and 2 g x x x 2 13 15, find( ) fxg . Show your work

Answer 1

`\begin{gathered} f(x)=4x^2+6x \\ g(x)=2x^2+13x+15 \end{gathered}`

Now

`((f)/(g)_{})(x)\text{ we are going to divide}`
`((f)/(g))(x)=(4x^2+6x)/(2x^2+13x+15)`
`(4x^2+6x)/(2x^2+13x+15)=(2x(2x+3))/(2x^2+13x+15)`

Now also factor the denominator

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

Cancel the common factor 2x+3

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

The final answer

`((f)/(g))(x)=(2x)/(x+5)`