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

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

Evalueren

$$-4$$

Korte oplossingsstappen

Vouw expressies uit en maak de bijbehorende noemers gelijk om expressies op te tellen of af te trekken. Kleinste gemene veelvoud van x+y en x-y is \left(x+y\right)\left(x-y\right). Vermenigvuldig \frac{x-y}{x+y} met \frac{x-y}{x-y}. Vermenigvuldig \frac{x+y}{x-y} met \frac{x+y}{x+y}.

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

Aangezien \frac{\left(x-y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} en \frac{\left(x+y\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)} dezelfde noemer hebben, kunt u ze aftrekken door hun tellers af te trekken.

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

Voer de vermenigvuldigingen uit in \left(x-y\right)\left(x-y\right)-\left(x+y\right)\left(x+y\right).

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

Combineer gelijke termen in x^{2}-xy-xy+y^{2}-x^{2}-xy-xy-y^{2}.

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

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

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

Vouw expressies uit en maak de bijbehorende noemers gelijk om expressies op te tellen of af te trekken. Vermenigvuldig 1 met \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}.

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

Aangezien \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} en \frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)} dezelfde noemer hebben, kunt u ze aftrekken door hun tellers af te trekken.

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

Voer de vermenigvuldigingen uit in \left(x+y\right)\left(x-y\right)-\left(x^{2}-xy-y^{2}\right).

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

Combineer gelijke termen in x^{2}-xy+yx-y^{2}-x^{2}+xy+y^{2}.

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

Deel \frac{-4xy}{\left(x+y\right)\left(x-y\right)} door \frac{xy}{\left(x+y\right)\left(x-y\right)} door \frac{-4xy}{\left(x+y\right)\left(x-y\right)} te vermenigvuldigen met de omgekeerde waarde van \frac{xy}{\left(x+y\right)\left(x-y\right)}.

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

Streep xy\left(x+y\right)\left(x-y\right) weg in de teller en in de noemer.

$$-4$$

Factoriseren

$$-4$$