rewrite x in g(x) to f(x)
[tex]g(f(x)) = g( \frac{1}{x - 6} ) \\ = \frac{7}{ \frac{1}{x - 6} - 1} + 6 \\ = \frac{7}{ \frac{1}{x - 6} - \frac{x - 6}{x - 6} } + 6 \\ = \frac{7}{ \frac{7 - x}{x - 6} } + 6 \\ = \frac{7(x - 6)}{7 - x} + 6 \\ = \frac{7(x - 6)}{7 - x} + \frac{6(7 - x)}{7 - x} \\ = \frac{7x - 42}{7 - x} + \frac{42 - 6x}{7 - x} \\ = \frac{x}{7 - x}[/tex]
