Question

Use the principle of mathematical induction to show that:

a_n = n/(n^2 + 1) is decreasing.

BASE CASE:
Show that n = 1 is true.
I did this

INDUCTION HYPOTHESIS
Assume n = k is true

=> a_k < a_k+1
=> (k)/(k^2 + 1) < (k+1)/((k+1)^2 + 1)

a_k = (k)/(k^2 + 1)

SHOW:
Show that n = k + 1 is true:
=> a_k+1 < a_k+2

=> (k+1)/((k+1)^2 + 1) < (k+2)/((k+2)^2 + 1)

I am stuck on this induction step. How do I "revive" the a_k expression on my LHS or RHS of the above expresion?