Question

Упростите выражение:
$\frac{1}{1-\frac{1}{1-\frac{1}{a+1} } } }$

Answer 1

$1-\frac{1}{a+1}=\frac{a+1-1}{a+1}=\frac{a}{a+1}\; ;\\\\\\\frac{1}{1-\frac{1}{a+1}}=\frac{1}{\frac{a}{a+1}}=\frac{a+1}{a}\; ;\\\\\\1-\frac{1}{1-\frac{1}{a+1}}=1-\frac{a+1}{a}=\frac{a-a-1}{a}=-\frac{1}{a}\; ;\\\\\\\frac{1}{1-\frac{1}{1-\frac{1}{a+1}}}=\frac{1}{-\frac{1}{a}}=-a\; .$