a+2−42−a=a+2- \dfrac {4}{2-a}= ___ .

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Worked solution

1. 利用分式的性质,将分母中的 $2-a$ 变形为 $-(a-2)$,将减法转化为加法

a+2−42−a=a+2+4a−2a+2- \dfrac {4}{2-a} = a+2+ \dfrac {4}{a-2}

2. 对整式 $a+2$ 进行通分,使其分母变为 $a-2$,在此过程中应用平方差公式

a+2=(a+2)(a−2)a−2=a2−4a−2a+2 = \dfrac{(a+2)(a-2)}{a-2} = \dfrac{a^2-4}{a-2}

3. 合并同分母分式并化简分子得到最终结果

a2−4a−2+4a−2=a2−4+4a−2=a2a−2\dfrac{a^2-4}{a-2} + \dfrac{4}{a-2} = \dfrac{a^2-4+4}{a-2} = \dfrac{a^2}{a-2}

Answer

a2a−2\dfrac{a^2}{a-2}

AI analysis — may contain mistakes.

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