$解:最简公分母为{(a-2)}^{2}(a+2)$
${\frac {a} {{a}^{2}-4}}={\frac {a} {(a-2)(a+2)}}={\frac {a(a-2)} {{(a-2)}^{2}(a+2)}}$
${\frac {a-1} {a-2}}={\frac {(a-1)(a-2)(a+2)} {{(a-2)}^{2}(a+2)}}$
${\frac {a+2} {{a}^{2}-4a+4}}={\frac {a+2} {{(a-2)}^{2}}}={\frac {{(a+2)}^{2}} {{(a-2)}^{2}(a+2)}}$