I think the nuances are right in front of you - just look at the verb by itself. For example, "sort" means to organise or put in order. "Work" means to make an effort. "Straighten" means to make something point directly. "Smooth" as a verb means to remove any roughness.

My interpretations: 1) "Sort out" implies there is some confusion. To 'sort out' means to work through the details and make sure the confusion is resolved. For example, we received conflicting customer requirements for a software product we are developing. We need to 'sort out' what the customer really wants. 2) "Straighten out" means that you've got some explaining to do. For example, something happened that shouldn't have and now you need to explain to the parties how to keep it from happening again. They need to be 'straightened out." 3) "Work something out" generally means there is a conflict between two parties that needs a solution. For example, my neighbor's dog barks at 5am. He and I need to 'work something out' so I can sleep. 4) "Smooth something over" means there is a fracas over something and you need to calm it down. For example, your mother insulted your mother-in-law. You have to go to your mother-in-law and 'smooth things over.' Then you go to your mother and 'straighten her out." :-) 5) "Get to the bottom of" is an investigation into some wrongdoing. For example, someone at work broke the copier and left it. You have to solve the mystery of who did it by 'getting to the bottom of it.' I hope this helps! Allen

>Bernadette >Jan >Peachey Thank you very much!! I think I got smooth over and get to the bottom of, but still have a hard time telling part sort out, straighten out, and work out in terms of their nuances.. ^^; It's harrrrrd! haha

Solve is more formal, like a mathematical problem, but it can be used informally also, like to solve a problem you had with a neighbor for example. Straighten out, is in my understanding to correct someone's mistake, or a situation that someone else has caused. For example my father has to straighten out my problems with the credit company because I have no money to give them. You can also straighten someone out. It means to force them, either verbally or physically to rectify a bad situation that they created. Often it can mean to beat someone up, so you simply straighten them out for whatever wrong they did to you. Work something out can be to work out the answer to a puzzle, or it can mean when two people work out their differences, especially in a relationship...see the Beatles song 'we can work it out' You can also work out what someone's motives are towards you...eg, 'I have worked out what she is doing'. Smooth something over is similar to straighten something out, but without the threat of violence, it means to try and make peace from a difficult situation, usually you smooth over someone else's mistake/bad behavior. Get to the bottom of something is like solving a mystery, so yes it can answer the question about motives or causes, for example getting to the bottom of a crime. These are just basic explanations, you should look into them a little deeper for more nuanced shades of meaning.

・sort out - to do something that fixes a problem. E.g., "Have you sorted out the seating arrangement yet?" ・straighten out - to put things in order, to organize something. ・work something out - solve something. "Have you worked out why the printer isn't working yet?" "Have you worked out the math problem yet?" ・smooth something over - you were correct! Calm down a troublesome situation. ・get to the bottom of -- Solving something by figuring out what caused it. "Have you gotten to the bottom of the mystery yet?"