If \({\rm{a}}\,{\rm{ + }}\,\frac{{\rm{1}}}{{\rm{b}}}\, = \,1\) and \({\rm{b}}\,{\rm{ + }}\,\frac{{\rm{1}}}{{\rm{c}}}\, = \,1\), then find the value of \({\rm{c}}\,{\rm{ + }}\,\frac{{\rm{1}}}{{\rm{a}}}\).

1
-1
2
1
3
b
4
-b

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