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