How do I do this reduction?

Question

I'm stuck on how to do this reduction, I have read this post and this pdf but I can't seem to find a solution: (λx.yx)((λy.λt.yt)zx)=> (λx.yx)(λt.zxt) => y(λt.zxt)

but the solution should be yx according to online solvers.

could someone explain what passages I am doing wrong? What are the passages that you should follow to do it right?

Answer 1

applicative order

β y := z

(λx.yx)((λy.λt.yt)zx) 
          =    =  =

(λx.yx)((λt.zt)x)

β t := x

(λx.yx)((λt.zt)x)
          =  = =

(λx.yx)(zx)

β x := zx

(λx.yx)(zx)
  =  = ====

y(zx)