解決xleft(y-1right)+yleft(1-xright)/left(x-1right)left(1-yright)-y-x/(x-1)(y-1) |Microsoft數學求解器

$$\frac{ x \left( y-1 \right) +y \left( 1-x \right) }{ \left( x-1 \right) \left( 1-y \right) } - \frac{ y-x }{ (x-1)(y-1) }$$

評估

$$\frac{2\left(y-x\right)}{\left(1-y\right)\left(x-1\right)}$$

簡短的解題步驟

若要對運算式相加或相減，請先通分使其分母相同。 \left(x-1\right)\left(1-y\right) 和 \left(x-1\right)\left(y-1\right) 的最小公倍式為 \left(x-1\right)\left(y-1\right)。 \frac{x\left(y-1\right)+y\left(1-x\right)}{\left(x-1\right)\left(1-y\right)} 乘上 \frac{-1}{-1}。

$$\frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)}{\left(x-1\right)\left(y-1\right)}-\frac{y-x}{\left(x-1\right)\left(y-1\right)}$$

因為 \frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)}{\left(x-1\right)\left(y-1\right)} 和 \frac{y-x}{\left(x-1\right)\left(y-1\right)} 的分母相同，所以將分子相減即可相減這兩個值。

$$\frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)-\left(y-x\right)}{\left(x-1\right)\left(y-1\right)}$$

計算 -\left(x\left(y-1\right)+y\left(1-x\right)\right)-\left(y-x\right) 的乘法。

$$\frac{-yx+x-y+yx-y+x}{\left(x-1\right)\left(y-1\right)}$$

合併 -yx+x-y+yx-y+x 中的同類項。

$$\frac{2x-2y}{\left(x-1\right)\left(y-1\right)}$$

展開 \left(x-1\right)\left(y-1\right)。

$$\frac{2x-2y}{xy-x-y+1}$$

展開

$$-\frac{2\left(y-x\right)}{\left(x-1\right)\left(y-1\right)}$$

簡短的解題步驟

若要對運算式相加或相減，請先通分使其分母相同。 \left(x-1\right)\left(1-y\right) 和 \left(x-1\right)\left(y-1\right) 的最小公倍式為 \left(x-1\right)\left(y-1\right)。 \frac{x\left(y-1\right)+y\left(1-x\right)}{\left(x-1\right)\left(1-y\right)} 乘上 \frac{-1}{-1}。

$$\frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)}{\left(x-1\right)\left(y-1\right)}-\frac{y-x}{\left(x-1\right)\left(y-1\right)}$$

因為 \frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)}{\left(x-1\right)\left(y-1\right)} 和 \frac{y-x}{\left(x-1\right)\left(y-1\right)} 的分母相同，所以將分子相減即可相減這兩個值。

$$\frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)-\left(y-x\right)}{\left(x-1\right)\left(y-1\right)}$$

計算 -\left(x\left(y-1\right)+y\left(1-x\right)\right)-\left(y-x\right) 的乘法。

$$\frac{-yx+x-y+yx-y+x}{\left(x-1\right)\left(y-1\right)}$$

合併 -yx+x-y+yx-y+x 中的同類項。

$$\frac{2x-2y}{\left(x-1\right)\left(y-1\right)}$$

展開 \left(x-1\right)\left(y-1\right)。

$$\frac{2x-2y}{xy-x-y+1}$$