$$\frac{x-1}{x^{2}-4}*\frac{x^{2}-4x+4}{x-1}$$
$\frac{x-2}{x+2}$
$$\frac{\left(x-1\right)\left(x^{2}-4x+4\right)}{\left(x^{2}-4\right)\left(x-1\right)}$$
$$\frac{x^{2}-4x+4}{x^{2}-4}$$
$$\frac{\left(x-2\right)^{2}}{\left(x-2\right)\left(x+2\right)}$$
$$\frac{x-2}{x+2}$$
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