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

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

Ovrednoti

$$\frac{3xy}{2\left(x^{2}-y^{2}\right)}$$

Kratka navodila za rešitev

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

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

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

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

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

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

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

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

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

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

Faktorizirajte 2x-2y.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x+y\right)\left(x-y\right) in 2\left(x-y\right) je 2\left(x+y\right)\left(x-y\right). Pomnožite \frac{xy}{\left(x+y\right)\left(x-y\right)} s/z \frac{2}{2}. Pomnožite \frac{y}{2\left(x-y\right)} s/z \frac{x+y}{x+y}.

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

\frac{2xy}{2\left(x+y\right)\left(x-y\right)} in \frac{y\left(x+y\right)}{2\left(x+y\right)\left(x-y\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Izvedi množenje v 2xy+y\left(x+y\right).

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

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

$$\frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

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

$$\frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)}-\frac{y^{2}}{2\left(x+y\right)\left(x-y\right)}$$

Ker \frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)} in \frac{y^{2}}{2\left(x+y\right)\left(x-y\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{y^{2}+3xy-y^{2}}{2\left(x+y\right)\left(x-y\right)}$$

Združite podobne člene v y^{2}+3xy-y^{2}.

$$\frac{3xy}{2\left(x+y\right)\left(x-y\right)}$$

Razčlenite 2\left(x+y\right)\left(x-y\right).

$$\frac{3xy}{2x^{2}-2y^{2}}$$

Faktoriziraj

$$\frac{3xy}{2\left(x^{2}-y^{2}\right)}$$