It says your model number NV59C (20v being Vietnamese correct?) supports 2 DIMMs of up to 4GB each. If you upgrade, buy two of the same sticks. Don't mix and match! Replace the old one and you should be fine. The ranks mean if it has chips on one side of the stick or both sides. I really don't think it matters too much. Shouldn't really worry. If you upgrade passed 4gb remember that you need a 64bit operating system (x64) to use all of it.
I bought a kit and a stick to test ; both cases work beautifully
I asked this question since lots of folks on newegg had to RMA due to those "rank" and "chip numbers" problems .
Who know my laptop is picky or not
And yes ; greeting from a Vietnamese friend
PS :AFAIK ; the ranks of the RAM is sometime different from the layout . I know it's a single one because the part number .