Réitigh x^-1+y^-1/x+y-x^-1-y^-1/x-y

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

Luacháil

$$\frac{2}{xy}$$

Céimeanna gearra réitigh

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de x+y agus x-y ná \left(x+y\right)\left(x-y\right). Méadaigh \frac{x^{-1}+y^{-1}}{x+y} faoi \frac{x-y}{x-y}. Méadaigh \frac{x^{-1}-y^{-1}}{x-y} faoi \frac{x+y}{x+y}.

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

Tá an t-ainmneoir céanna ag \frac{\left(x^{-1}+y^{-1}\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} agus \frac{\left(x^{-1}-y^{-1}\right)\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.

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

Déan iolrúcháin in \left(x^{-1}+y^{-1}\right)\left(x-y\right)-\left(x^{-1}-y^{-1}\right)\left(x+y\right).

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

Cumaisc téarmaí comhchosúla in: 1-\frac{1}{x}y+\frac{1}{y}x-1-1-\frac{1}{x}y+\frac{1}{y}x+1.

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

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

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

Scríobh 2\times \frac{1}{y} mar chodán aonair.

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

Scríobh \frac{2}{y}x mar chodán aonair.

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

Scríobh -2\times \frac{1}{x} mar chodán aonair.

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

Scríobh \frac{-2}{x}y mar chodán aonair.

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

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

$$\frac{\frac{2xx}{xy}+\frac{-2yy}{xy}}{x^{2}-y^{2}}$$

Tá an t-ainmneoir céanna ag \frac{2xx}{xy} agus \frac{-2yy}{xy} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\frac{2xx-2yy}{xy}}{x^{2}-y^{2}}$$

Déan iolrúcháin in 2xx-2yy.

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

Scríobh \frac{\frac{2x^{2}-2y^{2}}{xy}}{x^{2}-y^{2}} mar chodán aonair.

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana.

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

Cealaigh \left(x+y\right)\left(x-y\right) mar uimhreoir agus ainmneoir.

$$\frac{2}{xy}$$

Fairsingigh

$$\frac{2}{xy}$$

Céimeanna gearra réitigh

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de x+y agus x-y ná \left(x+y\right)\left(x-y\right). Méadaigh \frac{x^{-1}+y^{-1}}{x+y} faoi \frac{x-y}{x-y}. Méadaigh \frac{x^{-1}-y^{-1}}{x-y} faoi \frac{x+y}{x+y}.

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

Tá an t-ainmneoir céanna ag \frac{\left(x^{-1}+y^{-1}\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} agus \frac{\left(x^{-1}-y^{-1}\right)\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.

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

Déan iolrúcháin in \left(x^{-1}+y^{-1}\right)\left(x-y\right)-\left(x^{-1}-y^{-1}\right)\left(x+y\right).

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

Cumaisc téarmaí comhchosúla in: 1-\frac{1}{x}y+\frac{1}{y}x-1-1-\frac{1}{x}y+\frac{1}{y}x+1.

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

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

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

Scríobh 2\times \frac{1}{y} mar chodán aonair.

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

Scríobh \frac{2}{y}x mar chodán aonair.

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

Scríobh -2\times \frac{1}{x} mar chodán aonair.

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

Scríobh \frac{-2}{x}y mar chodán aonair.

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

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

$$\frac{\frac{2xx}{xy}+\frac{-2yy}{xy}}{x^{2}-y^{2}}$$

Tá an t-ainmneoir céanna ag \frac{2xx}{xy} agus \frac{-2yy}{xy} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\frac{2xx-2yy}{xy}}{x^{2}-y^{2}}$$

Déan iolrúcháin in 2xx-2yy.

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

Scríobh \frac{\frac{2x^{2}-2y^{2}}{xy}}{x^{2}-y^{2}} mar chodán aonair.

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana.

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

Cealaigh \left(x+y\right)\left(x-y\right) mar uimhreoir agus ainmneoir.

$$\frac{2}{xy}$$