Problem: The simplest form of 1β11+a1βa1-\dfrac{1}{1+\dfrac{a}{1-a}}1β1+1βaaβ1β is:
Answer Choices:
A. a if aβ 0a \neq 0aξ =0
B. 111
C. a if aβ β1a \neq-1aξ =β1
D. 1 - a with no restriction on a
E. aaa if aβ 1a \neq 1aξ =1 Solution:
1β(1βa)/(1βa+a)=1β1+a=a1-(1-a) /(1-a+a)=1-1+a=a1β(1βa)/(1βa+a)=1β1+a=a, provided aβ 1a \neq 1aξ =1.