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

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

Izračunaj

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Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+y i x-y jest \left(x+y\right)\left(x-y\right). Pomnožite \frac{x-y}{x+y} i \frac{x-y}{x-y}. Pomnožite \frac{x+y}{x-y} i \frac{x+y}{x+y}.

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

Budući da \frac{\left(x-y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} i \frac{\left(x+y\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz \left(x-y\right)\left(x-y\right)-\left(x+y\right)\left(x+y\right).

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

Kombinirajte slične izraze u x^{2}-xy-xy+y^{2}-x^{2}-xy-xy-y^{2}.

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

Rastavite x^{2}-y^{2} na faktore.

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

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Pomnožite 1 i \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}.

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

Budući da \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} i \frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz \left(x+y\right)\left(x-y\right)-\left(x^{2}-xy-y^{2}\right).

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

Kombinirajte slične izraze u x^{2}-xy+yx-y^{2}-x^{2}+xy+y^{2}.

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

Podijelite \frac{-4xy}{\left(x+y\right)\left(x-y\right)} s \frac{xy}{\left(x+y\right)\left(x-y\right)} tako da pomnožite \frac{-4xy}{\left(x+y\right)\left(x-y\right)} s brojem recipročnim broju \frac{xy}{\left(x+y\right)\left(x-y\right)}.

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

Skratite xy\left(x+y\right)\left(x-y\right) u brojniku i nazivniku.

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Faktor

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