a)
[tex]1+\frac{1}{1+x}
\\\\1+\frac{1}{1+\frac{41}{29}}
\\\\1+\frac{1}{\frac{29}{29}+\frac{41}{29}}
\\\\1+\frac{1}{\frac{70}{29}}
\\\\1+\frac{1}{\frac{70}{29}}[/tex]
[tex]\\\\\frac{\frac{70}{29}}{\frac{70}{29}}+\frac{1}{\frac{70}{29}}
\\\\\frac{1+\frac{70}{29}}{\frac{70}{29}}
\\\\\frac{\frac{29}{29}+\frac{70}{29}}{\frac{70}{29}}
\\\\\frac{\frac{99}{29}}{\frac{70}{29}}
\\\\\frac{99}{29*\frac{70}{29}}
[/tex]
[tex]\\\\\frac{99}{\frac{2030}{29}}
\\\\\frac{99}{70}[/tex]
b)
[tex](\sqrt2-1)(\sqrt2+1)
\\\sqrt2^2+(-1)(1)
\\2-1
\\1[/tex]
c)
[tex]1+\frac{1}{1+\sqrt2}
\\\\1+\frac{\sqrt2-1}{(\sqrt2-1)(\sqrt2+1)}
\\\\1+\frac{\sqrt2-1}{1}
\\\\1+\sqrt2-1
\\\\\sqrt2[/tex]