“Failure to provide information requested on this form may result in significant processing delays and/or the denial of your application.”
You're applying for a passport. You're looking at the application form, and you see this sentence.
Failure to provide information requested on this form may result in significant processing delays and/or the denial of your application.
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Failure to (do something) (may/will) result in (something)
Talk about what will happen if a person doesn't do something with this phrase. For example:
Failure to submit assignments by the due date will result in an automatic failing grade.
This means "If you don't submit your assignments by the due date, you will automatically get a failing grade."
This expression is very formal-sounding. People usually use this in formal written documents like applications, contracts, and so on.
provide (information or documents)
"Providing" information means giving information to an organization. Businesses, schools, hospitals, government offices, etc. may ask you to "provide" information about yourself:
Please provide your name, address, date of birth, and account number.
You will need to provide two forms of identification.
You can also use the phrase "provide (someone) with (something)":
You'll need to provide the bank with some proof of employment.
The word "significant" can mean "pretty large", "pretty long", "pretty strong", etc.
We use this word in the phrase "significant delays", which means that things are delayed for a pretty long time. Use this formal phrase to talk about things like traffic, shipping, business deals, etc.
process (an application/order/etc.)
After an organization receives something like an application, an order, a request, etc. they have to "process" it. "Processing" a document means reading it, entering some information into the proper computer systems, sending it to the right people, taking the correct actions, etc.
You can use it like this:
We are currently processing your request. We will contact you in 7-10 business days.
(something) and/or (something)
In formal English, we sometimes use the phrase "and/or":
Please alert your doctor if you experience dizziness and/or fever.
We use this phrase to mean "A" or "B" or "A and B". This expression is common in business writing and government documents.
deny (someone's) application
If you apply for something, but the organization you're applying to says "no", then they've "denied" your application:
My financial aid application was denied.
This phrase can be used when talking about applying for things from the government like financial assistance, licenses, permits, etc.
However, applying for a job is different. If you apply for a job but don't get it, the company hasn't "denied" your application.
The noun form of "deny" is "denial", so you can also talk about "denial of an application":
Denial of an application is final. You may not re-apply.