Whakaoti i te e/x-pi/y=A

$$\frac { e } { x } - \frac { \pi } { y } = A$$

Whakaoti mō A

$$A=\frac{ey-\pi x}{xy}$$

$$x\neq 0\text{ and }y\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te xy, arā, te tauraro pātahi he tino iti rawa te kitea o x,y.

$$ye-x\pi =Axy$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$Axy=ye-x\pi$$

Whakaraupapatia anō ngā kīanga tau.

$$Axy=-\pi x+ey$$

He hanga arowhānui tō te whārite.

$$xyA=ey-\pi x$$

Whakawehea ngā taha e rua ki te xy.

$$\frac{xyA}{xy}=\frac{ey-\pi x}{xy}$$

Mā te whakawehe ki te xy ka wetekia te whakareanga ki te xy.

$$A=\frac{ey-\pi x}{xy}$$

Whakawehe ey-\pi x ki te xy.

$$A=\frac{e}{x}-\frac{\pi }{y}$$

Whakaoti mō x

$$x=\frac{ey}{Ay+\pi }$$

$$y\neq 0\text{ and }\left(A=0\text{ or }y\neq -\frac{\pi }{A}\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te xy, arā, te tauraro pātahi he tino iti rawa te kitea o x,y.

$$ye-x\pi =Axy$$

Tangohia te Axy mai i ngā taha e rua.

$$ye-x\pi -Axy=0$$

Tangohia te ye mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-x\pi -Axy=-ye$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(-\pi -Ay\right)x=-ye$$

He hanga arowhānui tō te whārite.

$$\left(-Ay-\pi \right)x=-ey$$

Whakawehea ngā taha e rua ki te -\pi -yA.

$$\frac{\left(-Ay-\pi \right)x}{-Ay-\pi }=-\frac{ey}{-Ay-\pi }$$

Mā te whakawehe ki te -\pi -yA ka wetekia te whakareanga ki te -\pi -yA.

$$x=-\frac{ey}{-Ay-\pi }$$

Whakawehe -ye ki te -\pi -yA.

$$x=\frac{ey}{Ay+\pi }$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{ey}{Ay+\pi }\text{, }x\neq 0$$