Question

Hello, I need some help with this homework question please?HW Q10

Answer 1

Given the following expression:

`(x)/(x+1)+(2)/(x-2)`

The expression will be simplified as follows:

`\begin{gathered} =(x)/(x+1)*(x-2)/(x-2)+(2)/(x-2)*(x+1)/(x+1) \\ \\ =(x(x-2))/((x+1)(x-2))+(2(x+1))/((x-2)(x+1)) \\ \\ =(x^2-2x)/(x^2-x-2)+(2x+2)/(x^2-x-2) \\ \\ =(x^2-2x+2x+2)/(x^2-x-2) \\ \\ =(x^2+2)/(x^2-x-2) \end{gathered}`

So, the answer will be option B

`(x^(2)+2)/(x^(2)-x-2)`