\frac { x ^ { 3 } - 2 x ( x + 1 } { x ^ { 3 } - 1 }
評估
\frac{x\left(x^{5}-x^{2}-2x-2\right)}{x^{3}-1}
展開
\frac{x^{6}-x^{3}-2x^{2}-2x}{x^{3}-1}
圖表
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已復制到剪貼板
x^{3}-\frac{2x\left(x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}
因數分解 x^{3}-1。
\frac{x^{3}\left(x-1\right)\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{2x\left(x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}
若要對運算式相加或相減，請先通分使其分母相同。 x^{3} 乘上 \frac{\left(x-1\right)\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}。
\frac{x^{3}\left(x-1\right)\left(x^{2}+x+1\right)-2x\left(x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}
因為 \frac{x^{3}\left(x-1\right)\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} 和 \frac{2x\left(x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} 的分母相同，所以將分子相減即可相減這兩個值。
\frac{x^{6}+x^{5}+x^{4}-x^{5}-x^{4}-x^{3}-2x^{2}-2x}{\left(x-1\right)\left(x^{2}+x+1\right)}
計算 x^{3}\left(x-1\right)\left(x^{2}+x+1\right)-2x\left(x+1\right) 的乘法。
\frac{-2x+x^{6}-x^{3}-2x^{2}}{\left(x-1\right)\left(x^{2}+x+1\right)}
合併 x^{6}+x^{5}+x^{4}-x^{5}-x^{4}-x^{3}-2x^{2}-2x 中的同類項。
\frac{-2x+x^{6}-x^{3}-2x^{2}}{x^{3}-1}
展開 \left(x-1\right)\left(x^{2}+x+1\right)。
x^{3}-\frac{2x\left(x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}
因數分解 x^{3}-1。
\frac{x^{3}\left(x-1\right)\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{2x\left(x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}
若要對運算式相加或相減，請先通分使其分母相同。 x^{3} 乘上 \frac{\left(x-1\right)\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}。
\frac{x^{3}\left(x-1\right)\left(x^{2}+x+1\right)-2x\left(x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}
因為 \frac{x^{3}\left(x-1\right)\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} 和 \frac{2x\left(x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} 的分母相同，所以將分子相減即可相減這兩個值。
\frac{x^{6}+x^{5}+x^{4}-x^{5}-x^{4}-x^{3}-2x^{2}-2x}{\left(x-1\right)\left(x^{2}+x+1\right)}
計算 x^{3}\left(x-1\right)\left(x^{2}+x+1\right)-2x\left(x+1\right) 的乘法。
\frac{-2x+x^{6}-x^{3}-2x^{2}}{\left(x-1\right)\left(x^{2}+x+1\right)}
合併 x^{6}+x^{5}+x^{4}-x^{5}-x^{4}-x^{3}-2x^{2}-2x 中的同類項。
\frac{-2x+x^{6}-x^{3}-2x^{2}}{x^{3}-1}
展開 \left(x-1\right)\left(x^{2}+x+1\right)。
示例
二次方程式
{ x } ^ { 2 } - 4 x - 5 = 0
三角學
4 \sin \theta \cos \theta = 2 \sin \theta
線性方程
y = 3x + 4
算術
699 * 533
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}