Whakaoti i te (x-3/y-3)(z-3)=z

$$( \frac { x - 3 } { y - 3 } ) ( z - 3 ) = z$$

Whakaoti mō x

$$x=-\frac{9-yz}{z-3}$$

$$y\neq 3\text{ and }z\neq 3$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te y-3.

$$\left(x-3\right)\left(z-3\right)=z\left(y-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-3 ki te z-3.

$$xz-3x-3z+9=z\left(y-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te z ki te y-3.

$$xz-3x-3z+9=zy-3z$$

Me tāpiri te 3z ki ngā taha e rua.

$$xz-3x+9=zy-3z+3z$$

Pahekotia te -3z me 3z, ka 0.

$$xz-3x+9=zy$$

Tangohia te 9 mai i ngā taha e rua.

$$xz-3x=zy-9$$

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

$$\left(z-3\right)x=zy-9$$

He hanga arowhānui tō te whārite.

$$\left(z-3\right)x=yz-9$$

Whakawehea ngā taha e rua ki te z-3.

$$\frac{\left(z-3\right)x}{z-3}=\frac{yz-9}{z-3}$$

Mā te whakawehe ki te z-3 ka wetekia te whakareanga ki te z-3.

$$x=\frac{yz-9}{z-3}$$

Whakaoti mō y

$$\left\{\begin{matrix}y=\frac{xz-3x+9}{z}\text{, }&z\neq 3\text{ and }x\neq 3\text{ and }z\neq 0\\y\neq 3\text{, }&x=3\text{ and }z=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe y ki 3 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te y-3.

$$\left(x-3\right)\left(z-3\right)=z\left(y-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-3 ki te z-3.

$$xz-3x-3z+9=z\left(y-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te z ki te y-3.

$$xz-3x-3z+9=zy-3z$$

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

$$zy-3z=xz-3x-3z+9$$

Me tāpiri te 3z ki ngā taha e rua.

$$zy=xz-3x-3z+9+3z$$

Pahekotia te -3z me 3z, ka 0.

$$zy=xz-3x+9$$

Whakawehea ngā taha e rua ki te z.

$$\frac{zy}{z}=\frac{xz-3x+9}{z}$$

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

$$y=\frac{xz-3x+9}{z}$$

Tē taea kia ōrite te tāupe y ki 3.

$$y=\frac{xz-3x+9}{z}\text{, }y\neq 3$$