Can you recommend a book with techniques for solving hard algebra/arithmetic problems? I'm a university student who never really studied maths in high school (I did the basic courses, but because I'm dyslexic I was to embarrassed to try the harder courses) now I'm getting back into it, and, while I'm perfectly fine with understanding the advanced concepts and grasping the theoretical side of things, I have a lot of trouble with the arithmetic in the harder questions. A lot of this is due to my not really knowing a lot of the techniques used in manipulating terms in complex fractions and just generally not having a good set of problem solving tools to fall back on.
Can you recommend any books that deal with arithmetic techniques for more advanced problems?
just to give you an idea, here are some examples of question formats that I would like to practice:
number 1
$$
\frac{x^{2}}{y}+\frac{y^{2}}{x}
$$
where $x = 2 + \sqrt{3}$ and $y = 2 - \sqrt{3}$
Number 2
factorise $54x^3 + 16$
number 3
given that $$a^{2}+b^{2} = 7ab$$
express $$\left(\frac{a+b}{3}\right)^{2}$$
in terms of a and b. Hence show that $$\log\left (\frac{a+b}{3}\right )=\frac{1}{2}\left(\log a+\log b \right)$$
if would be especially great if it had lots of practice questions.
Thanks.

Have a look at 'How to solve it - George Polya'. It's more general but quite helpful.
