Answer
$\dfrac{t-1}{t^2-6t+10} $
Work Step by Step
We are given that $f(t)=\dfrac{t+1}{t^2-2t+2} $ and $a=2$
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-2) \\=\dfrac{t-2+1}{(t-2)^2-2(t-2)+2} \\=\dfrac{t-1}{t^2-6t+10} $
