TITLE: Multiplying using reciprocal, addition and subtraction
QUESTION [9 upvotes]: Let $a,b\in\mathbb{R}$. How can we compute $a\times b$ using only the following operations only (with any reals) : 

$\frac{1}{*}$ (inverse)
$*+*$ (addition)
$*-*$ (subtraction)

?

REPLY [4 votes]: Build first the square function, as follows.
If $x\neq -1,0$, then $\displaystyle x^2= \frac{1}{\frac{1}{x}-\frac{1}{x+1}}-x$
Squaring $0$ and $-1$ is trivial.
Now, $\displaystyle xy=\frac{(x+y)^2-(x-y)^2}{4}$