Whakaoti i te a-R/a=R/b

$$\frac { a - R } { a } = \frac { R } { b }$$

Whakaoti mō R

$$R=\frac{ab}{a+b}$$

$$a\neq -b\text{ and }a\neq 0\text{ and }b\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te ab, arā, te tauraro pātahi he tino iti rawa te kitea o a,b.

$$b\left(a-R\right)=aR$$

Whakamahia te āhuatanga tohatoha hei whakarea te b ki te a-R.

$$ba-bR=aR$$

Tangohia te aR mai i ngā taha e rua.

$$ba-bR-aR=0$$

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

$$-bR-aR=-ba$$

Whakaraupapatia anō ngā kīanga tau.

$$-Ra-Rb=-ab$$

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

$$\left(-a-b\right)R=-ab$$

Whakawehea ngā taha e rua ki te -a-b.

$$\frac{\left(-a-b\right)R}{-a-b}=-\frac{ab}{-a-b}$$

Mā te whakawehe ki te -a-b ka wetekia te whakareanga ki te -a-b.

$$R=-\frac{ab}{-a-b}$$

Whakawehe -ab ki te -a-b.

$$R=\frac{ab}{a+b}$$

Whakaoti mō a

$$a=\frac{Rb}{b-R}$$

$$R\neq 0\text{ and }b\neq 0\text{ and }R\neq b$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$b\left(a-R\right)=aR$$

Whakamahia te āhuatanga tohatoha hei whakarea te b ki te a-R.

$$ba-bR=aR$$

Tangohia te aR mai i ngā taha e rua.

$$ba-bR-aR=0$$

Me tāpiri te bR ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$ba-aR=bR$$

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

$$\left(b-R\right)a=bR$$

He hanga arowhānui tō te whārite.

$$\left(b-R\right)a=Rb$$

Whakawehea ngā taha e rua ki te b-R.

$$\frac{\left(b-R\right)a}{b-R}=\frac{Rb}{b-R}$$

Mā te whakawehe ki te b-R ka wetekia te whakareanga ki te b-R.

$$a=\frac{Rb}{b-R}$$

Tē taea kia ōrite te tāupe a ki 0.

$$a=\frac{Rb}{b-R}\text{, }a\neq 0$$