How to get rid of a tree acid, perhaps (9)

I believe the answer is:

eradicate

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'how to get rid' is the definition.
I can't judge whether this definition defines the answer.

'a tree acid perhaps' is the wordplay.
'perhaps' indicates an anagram.
'a'+'tree'+'acid'='atreeacid'
'atreeacid' is an anagram of 'ERADICATE'.

'of' acts as a link.

Can you help me to learn more?

(Other definitions for eradicate that I've seen before include "Get rid of, remove all traces" , "Exterminate, extinguish" , "Stamp out, remove all traces of" , "Excise" , "Root out" .)

I've seen this clue in the Sydney Morning Herald.

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