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

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

Luacháil

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

Céimeanna gearra réitigh

Fachtóirigh x^{2}-y^{2}.

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x+y\right)\left(x-y\right) agus x+y ná \left(x+y\right)\left(x-y\right). Méadaigh \frac{x}{x+y} faoi \frac{x-y}{x-y}.

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

Tá an t-ainmneoir céanna ag \frac{x^{2}}{\left(x+y\right)\left(x-y\right)} agus \frac{x\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Déan iolrúcháin in x^{2}-x\left(x-y\right).

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

Cumaisc téarmaí comhchosúla in: x^{2}-x^{2}+xy.

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

Fachtóirigh 2x-2y.

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x+y\right)\left(x-y\right) agus 2\left(x-y\right) ná 2\left(x+y\right)\left(x-y\right). Méadaigh \frac{xy}{\left(x+y\right)\left(x-y\right)} faoi \frac{2}{2}. Méadaigh \frac{y}{2\left(x-y\right)} faoi \frac{x+y}{x+y}.

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

Tá an t-ainmneoir céanna ag \frac{2xy}{2\left(x+y\right)\left(x-y\right)} agus \frac{y\left(x+y\right)}{2\left(x+y\right)\left(x-y\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

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

Déan iolrúcháin in 2xy+y\left(x+y\right).

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

Cumaisc téarmaí comhchosúla in: 2xy+xy+y^{2}.

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

Fachtóirigh 2x^{2}-2y^{2}.

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

Tá an t-ainmneoir céanna ag \frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)} agus \frac{y^{2}}{2\left(x+y\right)\left(x-y\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Cumaisc téarmaí comhchosúla in: y^{2}+3xy-y^{2}.

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

Fairsingigh 2\left(x+y\right)\left(x-y\right)

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

Fachtóirigh

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