$$\frac{2a-2}{a+2}\div\frac{a^{2}+a-2}{a^{2}-4}$$
$\frac{2\left(a-2\right)}{a+2}$
$$\frac{\left(2a-2\right)\left(a^{2}-4\right)}{\left(a+2\right)\left(a^{2}+a-2\right)}$$
$$\frac{2\left(a-2\right)\left(a-1\right)\left(a+2\right)}{\left(a-1\right)\left(a+2\right)^{2}}$$
$$\frac{2\left(a-2\right)}{a+2}$$
$$\frac{2a-4}{a+2}$$
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