B1. Simplify the expression $\frac{a^{2}-4}{a^{2}-4 a+4}: \frac{a^{2}+5 a+6}{a-2}-\frac{a^{6}-1}{a^{4}-a^{3}+a-1}: \frac{(a+3)\left(a^{2}+a+1\right)}{-a+1}+\frac{a^{n-1}}{a^{n}+3 a^{n-1}}$, where $a \in \mathbb{R}$ and simultaneously $|a|>3$.
B1. Factorize the expressions and extract the common factor $\frac{(a-2)(a+2)}{(a-2)(a-2)}: \frac{(a+2)(a+3)}{a-2}-\frac{\left(a^{3}-1\right)\left(a^{3}+1\right)}{\left(a^{3}+1\right)(a-1)}: \frac{(a+3)\left(a^{2}+a+1\right)}{-a+1}+$ $\frac{a^{n-1}}{a^{n-1}(a+3)}$. Simplify and divide $\frac{(a+2)}{(a-2)} \cdot \frac{(a-2)}{(a+2)(a+3)}-\frac{(a-1)\left(a^{2}+a+1\right)}{(a-1)} \cdot \frac{-a+1}{(a+3)\left(a^{2}+a+1\right)}+\frac{1}{a+3}$. Simplify to the form $\frac{1}{a+3}-\frac{-a+1}{a+3}+\frac{1}{a+3}$. Add and get the result $\frac{a+1}{a+3}$.

Factorization of the first part of the expression $\frac{(a-2)(a+2)}{(a-2)(a-2)}: \frac{(a+2)(a+3)}{a-2} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots$ point

Simplification of the first part of the expression to the form $\frac{(a+2)}{(a-2)} \cdot \frac{(a-2)}{(a+2)(a+3)}=\frac{1}{a+3} \ldots \ldots \ldots \ldots \ldots \ldots . .1$ point

Factorization of the second part of the expression $\frac{\left(a^{3}-1\right)\left(a^{3}+1\right)}{\left(a^{3}+1\right)(a-1)}: \frac{(a+3)\left(a^{2}+a+1\right)}{-a+1} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots$ point

Simplification of the second part of the expression to the form $\frac{(a-1)\left(a^{2}+a+1\right)}{(a-1)} \cdot \frac{-a+1}{(a+3)\left(a^{2}+a+1\right)}=\frac{-a+1}{a+3} \ldots \ldots . .1$ point

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