Problem:
If x=ba​,aî€ =b and bî€ =0, then a−ba+b​=
Answer Choices:
A. x+1x​
B. x−1x+1​
C. 1
D. x−x1​
E. x+x1​
Solution:
Since a=bx,a−ba+b​=bx−bbx+b​=b(x−1)b(x+1)​=x−1x+1​. To show that the other four choices are incorrect, let a=2 and b=1.
OR
Dividing numerator and denominator by b shows that
a−ba+b​=ba​−1ba​+1​=x−1x+1​
Note. More generally, if ts​=vuâ€‹î€ =1 then s−ts+t​=u−vu+v​, since both sides of the last equation equal vu​t−tvu​t+t​.