評估
-\frac{x^{3}+x^{2}+x+1}{x^{2}+2x-1}
展開
-\frac{x^{3}+x^{2}+x+1}{x^{2}+2x-1}
圖表
共享
已復制到剪貼板
\frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}-x
因數分解 x^{2}+2x-1。
\frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}-\frac{x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
若要對運算式相加或相減，請先通分使其分母相同。 x 乘上 \frac{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}。
\frac{x^{2}-2x-1-x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
因為 \frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)} 和 \frac{x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)} 的分母相同，所以將分子相減即可相減這兩個值。
\frac{x^{2}-2x-1-x^{3}-x^{2}\sqrt{2}-x^{2}-x^{2}+x^{2}\sqrt{2}+x}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
計算 x^{2}-2x-1-x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right) 的乘法。
\frac{-x^{2}-x-1-x^{3}}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
合併 x^{2}-2x-1-x^{3}-x^{2}\sqrt{2}-x^{2}-x^{2}+x^{2}\sqrt{2}+x 中的同類項。
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-\left(\sqrt{2}\right)^{2}+1}
展開 \left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)。
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-2+1}
\sqrt{2} 的平方是 2。
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-1}
將 -2 與 1 相加可以得到 -1。
\frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}-x
因數分解 x^{2}+2x-1。
\frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}-\frac{x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
若要對運算式相加或相減，請先通分使其分母相同。 x 乘上 \frac{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}。
\frac{x^{2}-2x-1-x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
因為 \frac{x^{2}-2x-1}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)} 和 \frac{x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)} 的分母相同，所以將分子相減即可相減這兩個值。
\frac{x^{2}-2x-1-x^{3}-x^{2}\sqrt{2}-x^{2}-x^{2}+x^{2}\sqrt{2}+x}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
計算 x^{2}-2x-1-x\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right) 的乘法。
\frac{-x^{2}-x-1-x^{3}}{\left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)}
合併 x^{2}-2x-1-x^{3}-x^{2}\sqrt{2}-x^{2}-x^{2}+x^{2}\sqrt{2}+x 中的同類項。
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-\left(\sqrt{2}\right)^{2}+1}
展開 \left(x-\left(\sqrt{2}-1\right)\right)\left(x-\left(-\sqrt{2}-1\right)\right)。
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-2+1}
\sqrt{2} 的平方是 2。
\frac{-x^{2}-x-1-x^{3}}{x^{2}+2x-1}
將 -2 與 1 相加可以得到 -1。
示例
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
算術
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矩陣
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
聯立方程
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
微分
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
積分
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
限制
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}