Mix two books up with film about bird racing machines (3,5)

I believe the answer is:

bmx bikes

'racing machines' is the definition.
(race bikes)

'mix two books up with film about bird' is the wordplay.
'two books' means two replacements for 'book'.
'book' becomes 'b' (abbreviation for book).
'book' becomes 'b' (abbreviation for book).
'up' indicates an anagram (letters get chucked up).
'with' means one lot of letters go next to another.
'film about bird' becomes 'Kes' (1969 film about a kestrel).
'mix'+'b'+'b'='mixbb'
'mixbb' is an anagram of 'bmxbi'.
'bmxbi'+'kes'='BMX BIKES'

I've seen this clue in The Times.

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