141. Given two 7-arithmetic functions

$$
f(x)=\frac{x+5}{5 x+1}, \quad g(x)=\frac{4 x+3}{6 x+3}
$$

Calculate $f(g(x))$ and $g(f(x))$.
141. We have

\[
\begin{aligned}
& f(g(x))=\frac{\frac{4 x+3}{6 x+3}+5}{5 \frac{4 x+3}{6 x+3}+1}=\frac{6 x+4}{5 x+4} \\
& g(f(x))=\frac{4 \frac{x+5}{5 x+1}+3}{6 \frac{x+5}{5 x+1}+3}=\frac{5 x+2}{5}=x+6
\end{aligned}
\]