解決x-y/x+y-x+y/x-y/1-frac{x^2-xy-y^2{x^2-y^2}} |Microsoft數學求解器

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

評估

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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。 x+y 和 x-y 的最小公倍式為 \left(x+y\right)\left(x-y\right)。 \frac{x-y}{x+y} 乘上 \frac{x-y}{x-y}。 \frac{x+y}{x-y} 乘上 \frac{x+y}{x+y}。

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

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

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

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

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

合併 x^{2}-xy-xy+y^{2}-x^{2}-xy-xy-y^{2} 中的同類項。

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{1-\frac{x^{2}-xy-y^{2}}{x^{2}-y^{2}}}$$

因數分解 x^{2}-y^{2}。

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{1-\frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)}}$$

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

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}-\frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)}}$$

因為 \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} 和 \frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)} 的分母相同，所以將分子相減即可相減這兩個值。

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{\left(x+y\right)\left(x-y\right)-\left(x^{2}-xy-y^{2}\right)}{\left(x+y\right)\left(x-y\right)}}$$

計算 \left(x+y\right)\left(x-y\right)-\left(x^{2}-xy-y^{2}\right) 的乘法。

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{x^{2}-xy+yx-y^{2}-x^{2}+xy+y^{2}}{\left(x+y\right)\left(x-y\right)}}$$

合併 x^{2}-xy+yx-y^{2}-x^{2}+xy+y^{2} 中的同類項。

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{xy}{\left(x+y\right)\left(x-y\right)}}$$

\frac{-4xy}{\left(x+y\right)\left(x-y\right)} 除以 \frac{xy}{\left(x+y\right)\left(x-y\right)} 的算法是將 \frac{-4xy}{\left(x+y\right)\left(x-y\right)} 乘以 \frac{xy}{\left(x+y\right)\left(x-y\right)} 的倒數。

$$\frac{-4xy\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)xy}$$

在分子和分母中同時消去 xy\left(x+y\right)\left(x-y\right)。

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因式分解

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