Conditional separator between "Previous Page" and "Next Page" image links?

Hello!

I’m interested in using this separator image in between my “Older Entries” and “Newer Entries” buttons. Obviously, I can simply insert the image in between the two, but it looks odd and off kilter when the other button is hidden on the first and last pages of content.

Currently, I’m using this bit of code in my index.php:

<center><?php next_posts_link('<img style="border-style: none;" src="https://www.what-the-fluff.com/wp-content/themes/WunderTheme/images/olderentries.png" />'); ?><?php previous_posts_link('<img style="border-style: none;" src="https://www.what-the-fluff.com/wp-content/themes/WunderTheme/images/newerentries.png" />'); ?></center>

Is there a fairly simple solution that will hide the separator image when it is not needed?

You can view my blog at https://www.What-the-Fluff.com

Thanks for your help!