kill(all)$

load(ntrig)$ load(atrig1)$

van=facebook.com/LearningCalculus$

           With the new magnets installed at the LHC, particle energies
           are higher than ever before and small black holes are  being
           measured before they evaporate emitting blue particles.
           Scientists make measurements and notice two functions:
                 red: the potential function f(x,a) and
                 green: the evaporation function g(x,a)
           One of the mathematicians combines the two functions to
           make a blue function that exactly matches the black hole
           data, discovering wormholes and winning a Nobel prize.

           Be that mathematician. Write down the blue function.

f(x,a):=(x+a)^2/(x-a)^2;

g(x,a):=f(cos(x),a)$ g(t,a);

h(x,a):=f(x,a)+g(x,a);

h(t,a);