Given the following expression:
[tex]\frac{x}{x+1}+\frac{2}{x-2}[/tex]
The expression will be simplified as follows:
[tex]\begin{gathered} =\frac{x}{x+1}*\frac{x-2}{x-2}+\frac{2}{x-2}*\frac{x+1}{x+1} \\ \\ =\frac{x(x-2)}{(x+1)(x-2)}+\frac{2(x+1)}{(x-2)(x+1)} \\ \\ =\frac{x^2-2x}{x^2-x-2}+\frac{2x+2}{x^2-x-2} \\ \\ =\frac{x^2-2x+2x+2}{x^2-x-2} \\ \\ =\frac{x^2+2}{x^2-x-2} \end{gathered}[/tex]
So, the answer will be option B
[tex]\frac{x^{2}+2}{x^{2}-x-2}[/tex]
