Crossword Genius

Doctor, I croak with cold — one's often seen at the bedside (5,5)

Ross

I believe the answer is:

clock radio

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'one's often seen at the bedside' is the definition.
I can't tell whether this definition defines the answer.

'doctor i croak with cold' is the wordplay.
'doctor' is an anagram indicator.
'with' says to put letters next to each other.
'i'+'croak'='icroak'
'icroak' put after 'cold' is 'coldicroak'.
'coldicroak' is an anagram of 'CLOCK-RADIO'.

Can you help me to learn more?

(Another definition for clock radio that I've seen is " Alarm".)

I've seen this clue in The Guardian.
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