There are various ways which can cause a request to be broken. The most common broken requests you'll find on most sites are 404 errors. 301's and 302's can sometimes also indicate a broken request. When a browser has to deal with a broken request it will "hang" for a short moment before it finally decides the file isn't available. In this short "hang" moment the browser will double-check if the file which causes an error is really there or not. This process creates unnecessary load time and will thus make your website slower as it could be, especially when you have many broken requests.
After using this tool and you've detected the broken requests on your page(s) you should simply replace or remove these requests from your page(s).
Seeing a 404 error means the browser can communicate with the server of the tested URL but could not find the file you were requesting. This usually means you either made a typing mistake in the URL or it means the requested file is not physically on the server.
Both 301's and 302's technically aren't broken requests; they are redirects. Redirects automatically transfer you to a particular URL via another URL, for instance from domain.com to www.domain.com. Sometimes though, they can actually indicate a broken request, for instance when the webmaster of the tested site has redirected his 404 errors to a custom error page. The browser will see this as a 301 instead of a 404 error. Also, even if your 301 errors aren't broken requests, you should still fix them when taking page speed into consideration because they slow your site down.
Redirects make your website slower because they do not directly request and download your file or page, instead they first follow a redirect from one URL to another before they can download the actual file.
The reason this test is slower as others on the site is because it will check every individual file and link your web page points to, even the external(other domains as your own) ones. It has to visit all these files and pages and check their availability.
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