29*. What is greater: \(\frac{23^{1873}+1}{23^{1974}+1}\) or \(\frac{23^{1974}+1}{23^{1975}+1}\) ?

30 *. Let \(|y| \neq 1\) and \(y \neq 0\). It is also known that

\[
x_{1}=\frac{y-1}{y+1}, \quad x_{2}=\frac{x_{1}-1}{x_{1}+1}, \quad x_{3}=\frac{x_{2}-1}{x_{2}+1}, \ldots
\]

What is \(y\), if \(x_{1974}=3\) ?

31 *. If the equalities hold

\[
x=\frac{a-b}{a+b}, \quad y=\frac{b-c}{b+c}, \quad z=\frac{c-a}{c+a}
\]

then \((1+x)(1+y)(1+z)=(1-x)(1-y)(1-z)\). Prove it.
29. The first fraction is larger. Hint. You can use the substitution \(m=23^{1973}\) and find the difference between the fractions.