The easier way to do this would be to insert a Content Editor Web Part anywhere on the page for which you would like to hide the Quick Launch and insert the code in the HTML Source section of the web part. However, once in a while I face a couple of things with the Content Editor Web Part since we upgraded to SharePoint 2010. And that is that it many times adds blank lines, creating empty, blank spaces on my pages, or it changes my HTML code once I save the web part or page. So I prefer to put the code on a text file (you can use your computer's notepad and that should suffice) that I then upload to some document library on the site. Then I use the Content Editor Web Part to reference the file where I have saved the code. In this way I can prevent both SharePoint from "compiling" and changing my code to whatever, and I avoid the bug that adds blank lines to my pages where the Content Editor Web Part displays. But this is my preference. You can do whatever feels better, easier, or more comfortable for you.

The code you need is, as follows,