[tex]\frac{1}{1+a+b^{-1} } + \frac{1}{1+a+b^{-1} } + \frac{1}{1+a+b^{-1} } = 1\\\\\\frac{1}{1+a+\frac{1}{b}} + \frac{1}{1+a+\frac{1}{c}} + \frac{1}{1+a+\frac{1}{a}}\\\\since \\\\ abc = 1 \\\\ab=\frac{1}{c} \\\\\frac{1}{\frac{ab+b+1}{b} } + \frac{1}{1+b+ab} + \frac{1}{1+\frac{1}{ab} + \frac{1}{a}}\\\\ \frac{ab+b+1}{ab+b+1} = 1 = rhs \\ \\\\hence proved[/tex]

answer for question 1