(define $f
  (lambda [$z]
    (/ (+ (* a z) b) (+ (* c z) d))))

(define $f1
  (lambda [$z]
    (+ z (/ d c))))

(define $f2
  (lambda [$z]
    (/ 1 z)))

(define $f3
  (lambda [$z]
    (* z
       (/ (* -1 (- (* a d) (* b c)))
          c^2))))

(define $f4
  (lambda [$z]
    (+ (/ a c) z)))

(f4 (f3 (f2 (f1 z))))
;(/ (+ (* a z) b) (+ (* c z) d))