Express $\frac{x+1}{x^2-x} - \frac{x-1}{x^2+x}$as a fraction in its lowest terms.

Im guessing the question means factorizing that equation,
and i got this answer and i have no confident that it is right.
$\frac{4}{x^2-1}$

2. $\frac{x+1}{x^2-x} - \frac{x-1}{x^2+x}$

$\frac{x+1}{x(x-1)} - \frac{x-1}{x(x+1)}$

$\left ( \frac{x+1}{x(x-1)}\cdot\frac{x+1}{x+1} \right ) - \left ( \frac{x-1}{x(x+1)}\cdot \frac{x-1}{x-1}\right )$

$\frac{(x+1)^2}{x(x-1)(x+1)} - \frac{(x-1)^2}{x(x-1)(x+1)}$

$\frac{(x+1)^2-(x-1)^2}{x(x-1)(x+1)}$

$\frac{4\not x}{\not x(x-1)(x+1)}$

$\frac{4}{(x-1)(x+1)}$

$\frac{4}{x^2-1}$

You're right