+2864 Evaluate \(c+\frac{1}{a}\) if \(a+\frac{1}{b}=1\), and \(b+\frac{1}{c}=1 \).
Me so far:
ab+1=b
b=-1/c+1
a(-1/c+1)+1=-1/c+1
-a/c+a=-1/c
a/c-a=1/c
a-ac=1 ????
+129899 Evaluate c + 1/a
a + 1/b = 1 b + 1/c = 1
a = 1 - 1/b 1/c = 1 - b
a = (b - 1) c = 1
_____ ____
b 1 - b
1/a = b
____
b - 1
So
c + 1/a =
1 + b
____ ____ = [factor a negative out of the second denominator ]
(1 - b) b - 1
1 - b
____ _______ =
1 - b 1 - b
( 1 - b)
______ =
(1 - b)
1
