How to implement linear-fractional functions in cvx?

How can I implement the following in cvx:
f(x)=(Ax+b)/(c^{T}x+d) where dom(f)=\{x|c^{T}x+d>0\}. x is an optimization variable while A, b, c, and d are known constants.

You cannot. Linear fractional functions are not convex, even on that restricted domain. However, they are quasiconvex (indeed, quasilinear), which means that models involving these functions can often be solved using convex optimization—by transforming the problem into convex form, or by solving a sequence of convex optimization problems. CVX will not, however, perform these manipulations for you. I recommend consulting the book Convex Optimization by Boyd & Vandenberghe for discussions on both quasiconvexity and linear-fractional functions.