Is there any article needed for risk and farming business in the following sentence?
(A) Risk is an important aspect of (the) farming business.
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You can use either article in that sentence, and it would be grammatical.
Risk is an important aspect of a farming business.
This is talking about risk on a small-scale; it is saying that a farming business has a lot of inherent risk.
Risk is an important aspect of the farming business.
This is talking about risk on a grander scale; it is saying that the entire farming industry has much risk.
You could also make the sentence more generic by using no article, but, in that case, you would omit the word business:
Risk is an important aspect of farming.
This sentence could apply to a single farm, a single farming business, or the entire farming industry as a whole.
As for risk, it's best not to use an article when speaking about risk in general. If you are talking about specific risks, though, use the appropriate article:
A big risk in the farming business is price volatility.
Drought is the biggest risk faced by most farmers in this valley.