Students in high school, or university kids without embedded math knowledge, take note: Microsoft's Live Search can solve math equations with variables.

If you've got any interest in Microsoft's Live Search engine, Microsoft has pushed out an official Firefox extension that adds Live Search auto suggestions to your Firefox search box. It seems unlikely that many folks using Firefox are all that interested in Live Search, but if you happen to fall into that category, then this unholy marriage is for you.

Microsoft's Live image search tool added a new button underneath every image result you mouse over: "Show similar images." Close to the functionality of previously mentioned engine TinEye, but with a much wider scope and reach. The complexity of the image, and cleverness of its knock-offs, will of course vary from search to search, but if you're looking for a higher-res or non-marked-up copy of a certain graphic, Live seems pretty spot-on. Got your own dupe-finding tool for web images? Tell us about it in the comments.

Free alert service Exactfactor tracks search engine results by key words, and can email anyone interested in how any web site is doing in the battle for the top Google, Yahoo, or Live.com spot. After signing up for an account, you enter one or two web sites and key words to track them by. You'll see an instant report on the site's ranking on each search site, and can hit "Get alerts" to be e-mailed when that site improves, declines, or hits the front page of the search results. If you're looking for ways to juice your standing in the world of web search (or bury something unfortunate), check Tamar's guide to managing your online reputation.

The Digital Inspiration blog points out some really cool uses of Microsoft's Live Search engine, including the hasfeed: operator that does what it sounds like: Filters your results to only sites that have live RSS feeds. It's a great tool for feeding your job search reader, and Amit has four other neat Live Search hacks.