Answer
$$\dfrac{t-1}{t^2-2t+5} $$
Work Step by Step
We are given that $f(t)=\dfrac{t}{t^2+4}$ and $a=1$
When $a$ has a positive value then , shift the function to the right for $a$ units and when $a$ has a negative value then , shift the function to the left for $a$ units
Now, $f(t-a) =f(t-1) \\=\dfrac{t-1}{(t-1)^2+4} \\=\dfrac{t-1}{t^2-2t+5} $
