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

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

Arvuta

$$-4$$

Lühike lahenduskäik

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. x+y ja x-y vähim ühiskordne on \left(x+y\right)\left(x-y\right). Korrutage omavahel \frac{x-y}{x+y} ja \frac{x-y}{x-y}. Korrutage omavahel \frac{x+y}{x-y} ja \frac{x+y}{x+y}.

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

Kuna murdudel \frac{\left(x-y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} ja \frac{\left(x+y\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)} on sama nimetaja, lahutage nende lugejad.

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

Tehke korrutustehted võrrandis \left(x-y\right)\left(x-y\right)-\left(x+y\right)\left(x+y\right).

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

Kombineerige sarnased liikmed avaldises x^{2}-xy-xy+y^{2}-x^{2}-xy-xy-y^{2}.

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

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

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 1 ja \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}.

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

Kuna murdudel \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} ja \frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)} on sama nimetaja, lahutage nende lugejad.

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

Tehke korrutustehted võrrandis \left(x+y\right)\left(x-y\right)-\left(x^{2}-xy-y^{2}\right).

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

Kombineerige sarnased liikmed avaldises x^{2}-xy+yx-y^{2}-x^{2}+xy+y^{2}.

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

Jagage \frac{-4xy}{\left(x+y\right)\left(x-y\right)} väärtusega \frac{xy}{\left(x+y\right)\left(x-y\right)}, korrutades \frac{-4xy}{\left(x+y\right)\left(x-y\right)} väärtuse \frac{xy}{\left(x+y\right)\left(x-y\right)} pöördväärtusega.

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

Taandage xy\left(x+y\right)\left(x-y\right) nii lugejas kui ka nimetajas.

$$-4$$

Lahuta teguriteks

$$-4$$