Symbolic programming for dummies

Hi, I would like to try out symbolic programming. I know maple,
mathematica and others are computer algebra system that let you do
that, but they are not primitive languages. I would like to write and
run a very simple program [something like expanding (x^2 + 3)^2/(x)]
but written in a language like C or C++ or other. Do you know which is
the best and easiest programming language for symbolic computation?
And is there like a book which teaches symbolic math programming (I
know there are books who present general algorithms like the book of
Symbolic Integration by Bronstein, but this is of little use to me
now, because it's not fully practical, I need something like symbolic
programming for dummies with all details). Thanks
.

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