Selesaikan x-y/x+y-x+y/x-y/1-frac{x^2-xy-y^2{x^2-y^2}}

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

Nilaikan

$$-4$$

Langkah Penyelesaian Pendek

Untuk menambah atau menolak ungkapan, kembangkannya untuk membuat penyebut mereka sama. Gandaan sepunya terkecil x+y dan x-y ialah \left(x+y\right)\left(x-y\right). Darabkan \frac{x-y}{x+y} kali \frac{x-y}{x-y}. Darabkan \frac{x+y}{x-y} kali \frac{x+y}{x+y}.

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

Oleh kerana \frac{\left(x-y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} dan \frac{\left(x+y\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)} mempunyai penyebut yang sama, tolakkan dengan menolakkan pengangka.

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

Lakukan pendaraban dalam \left(x-y\right)\left(x-y\right)-\left(x+y\right)\left(x+y\right).

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

Gabungkan sebutan serupa dalam x^{2}-xy-xy+y^{2}-x^{2}-xy-xy-y^{2}.

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

Faktor x^{2}-y^{2}.

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

Untuk menambah atau menolak ungkapan, kembangkannya untuk membuat penyebut mereka sama. Darabkan 1 kali \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}.

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

Oleh kerana \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} dan \frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)} mempunyai penyebut yang sama, tolakkan dengan menolakkan pengangka.

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

Lakukan pendaraban dalam \left(x+y\right)\left(x-y\right)-\left(x^{2}-xy-y^{2}\right).

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

Gabungkan sebutan serupa dalam x^{2}-xy+yx-y^{2}-x^{2}+xy+y^{2}.

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

Bahagikan \frac{-4xy}{\left(x+y\right)\left(x-y\right)} dengan \frac{xy}{\left(x+y\right)\left(x-y\right)} dengan mendarabkan \frac{-4xy}{\left(x+y\right)\left(x-y\right)} dengan salingan \frac{xy}{\left(x+y\right)\left(x-y\right)}.

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

Batalkanxy\left(x+y\right)\left(x-y\right) pada kedua-dua pengangka dan penyebut.

$$-4$$

Faktor

$$-4$$