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