Splitting a PDF sounds like a tiny job: keep pages 4 to 9, download, done. The trouble starts when the document has a cover page, Roman-numeral front matter, or scanned pages with their own printed numbers. Page 4 in the PDF viewer may not be the page marked "4" in the document.
Before splitting, open the file and count from the actual first page of the PDF. If there is a cover sheet, that cover is page 1 for the tool even if the printed document starts later. Write down the ranges you want, then enter them in a simple format such as 1-3, 7, 10-12.
Pagivo's Split PDF tool keeps the selected pages in their original quality. It does not re-render the PDF, so text stays selectable and images keep their original resolution.