Convert non-convex optimization problems into convex optimization problems

Question

Let A ∈ Rm×n, b ∈ Rm, c ∈ Rn, and d ∈ R. Prove that the nonconvex optimization problem min x∈Rn ∥Ax−b∥/(c⊤x +d) subject to ∥x∥ ≤ 1;cTx+d > 0 is equivalent to the convex optimization problem min (y∈Rn , t) ∥Ay −bt∥ subject to ∥y∥ ≤ t; c⊤y +dt = 1