Question 1190750
Assume it is: 

if {{{a= (b-1)/(b+1)}}} and {{{b= 1/(1c^2)}}} express a in terms of c. 
:
The "1" in the denominator of the b= expression is meaningless so write it
{{{a= (b-1)/(b+1)}}} and {{{b= 1/(c^2)}}}
substitute 1/c^2 for b
{{{a = ((1/c^2)-1)/((1/c^2)+1)}}}
which is
{{{a = ((1-c^2)/c^2)/((1+c^2)/c^2)}}}
dividing fractions, invert the dividing fraction and multiply
{{{a = ((1-c^2)/c^2)*(c^2/(1+c^2))}}}
cancel c^2
{{{a = ((1-c^2)/(1+c^2))}}}