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将 $$$x^{2}$$$ 除以 $$$\left(x - 1\right) \left(x + 1\right)$$$
您的输入
使用长除法计算$$$\frac{x^{2}}{\left(x - 1\right) \left(x + 1\right)}$$$。
解答
将除数改写为：$$$\left(x - 1\right) \left(x + 1\right) = x^{2} - 1$$$。
将题目写成特殊格式（缺失项写为零系数）：
$$$\begin{array}{r|r}\hline\\x^{2}-1&x^{2}+0 x+0\end{array}$$$
步骤 1
将被除式的首项除以除式的首项: $$$\frac{x^{2}}{x^{2}} = 1$$$.
将计算结果写在表格的上部。
将其乘以除数：$$$1 \left(x^{2}-1\right) = x^{2}-1$$$。
从得到的结果中减去被除数：$$$\left(x^{2}\right) - \left(x^{2}-1\right) = 1$$$
$$\begin{array}{r|rrr:c}&{\color{DarkBlue}1}&&&\\\hline\\{\color{Magenta}x^{2}}-1&{\color{DarkBlue}x^{2}}&+0 x&+0&\frac{{\color{DarkBlue}x^{2}}}{{\color{Magenta}x^{2}}} = {\color{DarkBlue}1}\\&-\phantom{x^{2}}&&&\\&x^{2}&+0 x&-1&{\color{DarkBlue}1} \left(x^{2}-1\right) = x^{2}-1\\\hline\\&&&1&\end{array}$$由于余式的次数小于除式的次数，故除法完成。
所得表格再次显示如下：
$$\begin{array}{r|rrr:c}&{\color{DarkBlue}1}&&&\text{提示}\\\hline\\{\color{Magenta}x^{2}}-1&{\color{DarkBlue}x^{2}}&+0 x&+0&\frac{{\color{DarkBlue}x^{2}}}{{\color{Magenta}x^{2}}} = {\color{DarkBlue}1}\\&-\phantom{x^{2}}&&&\\&x^{2}&+0 x&-1&{\color{DarkBlue}1} \left(x^{2}-1\right) = x^{2}-1\\\hline\\&&&1&\end{array}$$因此，$$$\frac{x^{2}}{\left(x - 1\right) \left(x + 1\right)} = 1 + \frac{1}{\left(x - 1\right) \left(x + 1\right)}$$$。
答案
$$$\frac{x^{2}}{\left(x - 1\right) \left(x + 1\right)} = 1 + \frac{1}{\left(x - 1\right) \left(x + 1\right)}$$$A
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