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

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

Ovrednoti

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Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x+y in x-y je \left(x+y\right)\left(x-y\right). Pomnožite \frac{x-y}{x+y} s/z \frac{x-y}{x-y}. Pomnožite \frac{x+y}{x-y} s/z \frac{x+y}{x+y}.

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

Ker \frac{\left(x-y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} in \frac{\left(x+y\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v \left(x-y\right)\left(x-y\right)-\left(x+y\right)\left(x+y\right).

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

Združite podobne člene v x^{2}-xy-xy+y^{2}-x^{2}-xy-xy-y^{2}.

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

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

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Pomnožite 1 s/z \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}.

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

Ker \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} in \frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v \left(x+y\right)\left(x-y\right)-\left(x^{2}-xy-y^{2}\right).

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

Združite podobne člene v x^{2}-xy+yx-y^{2}-x^{2}+xy+y^{2}.

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

Delite \frac{-4xy}{\left(x+y\right)\left(x-y\right)} s/z \frac{xy}{\left(x+y\right)\left(x-y\right)} tako, da pomnožite \frac{-4xy}{\left(x+y\right)\left(x-y\right)} z obratno vrednostjo \frac{xy}{\left(x+y\right)\left(x-y\right)}.

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

Okrajšaj xy\left(x+y\right)\left(x-y\right) v števcu in imenovalcu.

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Faktoriziraj

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