Answer
$\dfrac{4}{5(x-1)} $
Work Step by Step
We apply Method 1 (A51), to treat the numerator and denominator of the complex rational expression separately. So by factoring both the denominator and numerator of each rational function and cancelling the common factors, we have
$$
\frac{\frac{8x}{x^2-1}}{\frac{10x}{x+1}}= \frac{\frac{8x}{(x+1)(x-1)}}{\frac{10x}{x+1}}= \frac{8x}{(x+1)(x-1)}\frac{x+1}{10x}\\
=\frac{4}{5(x-1)}
.$$
