The way they lay this out is quite “rapid fire” and I got stuck here too. To clear it up a little, you just have to think of Δk/k as a single variable.
Remove the Δy/y from the first line so you have Δk/k=ΔA/A +αΔk/k
Then you can use basic algebra to move α(Δk/k) over to the LHS.