The important redundancy

Algebra Level 2

f(x)=9x9x+3\large f(x)=\frac{9^x}{9^x+3}

Suppose we define f(x)f(x) as above. Let a=f(x)+f(1x)a=f(x)+f(1-x) and b=f(11996)+f(21996)+f(31996)++f(19951996).b=f\left(\frac1{1996}\right) + f\left(\frac2{1996}\right) + f\left(\frac3{1996}\right)+\ldots+ f\left(\frac{1995}{1996}\right).

Evaluate a+ba + b.

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