Learning to re-arrange, simplify, change subject of very complex algebra?

Hi there

I have posted on a similar theme before. I am 32 and have a degree in Mechanical Engineering, but took a foundation route rather than English A-Levels. There was also an 8 year gap between the foundation course, and the 'GCSE' grades I took aged 16 which would have covered basic algebra.

Because of this, I think I forgot, or failed to learn, the keys to a lot of basic algebraic manipulation. Im fine with straightforward examples of re-arranging, simplifying, factoring, making so-and-so the subject - but as soon as the examples become complex, and require a number of steps and techniques, I am totally scuppered.

I have got 6 books on basic algebra from the library, and the examples they have are all very simple and I can understand them. But in many of the maths problems I am trying in an A-Level textbook, and indeed in many of the engineering problems I remember at uni, they require you to do multiple things and to see certain relationships that it seems you either have the 'knack' for, or you don't. I want that knack!

Can anyone recommend a book that would present numerous multi-step worked examples of algebraic manipulation? How do other people usually develop this capacity? It feels like solving so many of these things is more like solving a puzzle rather than applying a simple rule, or spotting which of several rules you need to apply in a given example.

Not explaining myself very well, apologies.

How to use Advanced Algebra II
Free educational resource, available under a Creative Commons License. I'm not sure if this is what you are looking for, but it's free, so it can't hurt to take a look.

Also, I used Schaum's Outlines for self-study of Probability and Statistics. I liked it and they have ~60 books in the mathematics category. McGraw-Hill Professional - Mathematics (They had a couple of those at my library, and I'm Dutch, so if you're English you can probably find some in yours too.)

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How do other people usually develop this capacity?

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Practice makes perfect. Do a lot of exercises until you feel you get it.

Finally, I'd like to add that you actually are explaining yourself very well. What you're describing is more or less what I personally feel is mathematics: The puzzle of combining various rules/methods to solve a problem.

I would highly reccomend the cheap Schaum's Outlines books. Schaum's "Intermediate Algebra", is probably the book you are looking for. Lots of exercises, and all the answers.

Unfortunately it means sitting down and slogging through the whole book, but just set aside an hour each day to try some problems. You will get better.

Also remember that there will always be rules and "tricks" that will not be apparent to you, and it may frustrate you when the answer uses a method not stated specifically in the book. This is normal, and will become more frequent the deeper you go. You don't have a sponge-like brain anymore, which makes things worse. It's harder to remember stuff, which is why "drill" books like Schaum's are good, but you just need to put the effort in. You will get better.