Is it possible to file a patent which contains a combination of an already patented idea and a totally new idea,with the whole combination performing a different task and working under a differed principle from the original invention.

I would like to put three lights and the fan in the bathroom on one switch. Currently two lights are on one switch and then the third light and fan have their own switch. My plan is to tie the third light and fan into the light above the sink. Just wanted to check if there is any issues with this.

I can't seem to get the right answer for this equation... can you help me? 4(3a+2b)(2b-a)-5a(2a-b)

My main stack/vent which penetrates my roof is 4" plastic. It comes down vertical until it gets to the first floor ceiling where is turns 90 deg and runs horizontal to an outside wall. About 3 feet from this 90 deg elbow there is a "Y" connection for a toilet. I'm not sure but I assume at the...