Question

Hello I need help with this I’m in a rush

Answer 1

Recall that:

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

Now, we know that

`\begin{gathered} ((f)/(g))(x)=(x+4)/(x^2+2x), \\ f(x)=(1)/(x)\text{.} \end{gathered}`

Therefore,

`((1)/(x))/(g(x))=(x+4)/(x^2+2x).`

Solving the above equation for g(x) we get:

`g(x)=((1)/(x))/((x+4)/(x^2+2x)).`

Simplifying the above result we get:

`g(x)=(x^2+2x)/(x(x+4))=(x+2)/(x+4).`

Answer:

`g(x)=(x+2)/(x+4)\text{.}`