To render easier second hint provided inside (8)

I believe the answer is:

simplify

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'to render easier' is the definition.
I can't tell whether this defines the answer.

'second hint provided inside' is the wordplay.
'second' becomes 's' (common abbreviation).
'hint' becomes 'imply' (I've seen this before**).
'provided' becomes 'if'.
'inside' means one lot of letters goes inside another.
'imply' going around 'if' is 'implify'.
's'+'implify'='SIMPLIFY'

Can you help me to learn more?

(Other definitions for simplify that I've seen before include "Make accessible" , "Popularise" , "Reduce in complexity" , "Make less complex" , "Streamline" .)

I've seen this clue in The Telegraph.

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