$$\frac{a^{2}-2ab+b^{2}}{a^{2}-1}\cdot\frac{a-1}{a-b}$$
$\frac{a-b}{a+1}$
$$\frac{\left(a^{2}-2ab+b^{2}\right)\left(a-1\right)}{\left(a^{2}-1\right)\left(a-b\right)}$$
$$\frac{\left(a-1\right)\left(a-b\right)^{2}}{\left(a-1\right)\left(a+1\right)\left(a-b\right)}$$
$$\frac{a-b}{a+1}$$
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$-\frac{b-a}{a+1}$
