[tex]\bf g(x)=\cfrac{x+14}{x+2}~\hspace{8em}g(~~g(x)~~)=\cfrac{g(x)+14}{g(x)+2}\\\\\\(~~g(x)~~)=\cfrac{~~\frac{x+14}{x+2}+14~~}{\frac{x+14}{x+2}+2}\implies (~~g(x)~~)=\cfrac{~~\frac{x+14~~+14x+28}{x+2}~~}{\frac{x+14~~+2x+4}{x+2}}\\\\\\(~~g(x)~~)=\cfrac{~~\frac{15x+42}{x+2}~~}{\frac{3x+18}{x+2}}\implies (~~g(x)~~)=\cfrac{15x+42}{\underline{x+2}}\cdot \cfrac{\underline{x+2}}{3x+18}\\\\\\(~~g(x)~~)=\cfrac{15x+42}{3x+18}\implies (~~g(x)~~)=\cfrac{3(5x+14)}{3(x+6)}\implies (~~g(x)~~)=\cfrac{5x+14}{x+6}[/tex]
