Calculate the speed of the pulse from the following:

y(x,t) = 2/((x - 3t)^2 + 1)

Well the speed of the pulse is given by:

y(x,t) = f (x - vt) for a pulse traveling to the right and
y(x,t) = f (x + vt) for a pulse traveling to the left but in this case the function is (x - 3t)^2 so would the pulse speed be (3)^2 = 9 m/s ???

No. The speed is 3, to the right.