Answer
$\displaystyle \frac{4}{5x(x-1)}$
Work Step by Step
$...=\displaystyle \frac{8x}{x^{2}-1}\div\frac{10x}{x+1}=\frac{8x}{x^{2}-1}\cdot\frac{x+1}{10x}$
Factoring,
$8=4\cdot 2$
$10=5\cdot 2$
$ x^{2}-1=(x+1)(x-1)\quad$ (a difference of squares)
$x^{2}=x\cdot x$
... = $\displaystyle \frac{4\cdot 2\cdot x\cdot(x+1)}{(x+1)(x-1)\cdot 5\cdot 2\cdot x\cdot x}$
... cancel the following from both sides of the fraction line:
$2,\ x$, $(x+1)$
... = $\displaystyle \frac{4}{5x(x-1)}$
