Whakaoti i te 3z/m+n/b=f

$$\frac { 3 z } { m } + \frac { n } { b } = f$$

Whakaoti mō b

$$\left\{\begin{matrix}b=-\frac{mn}{3z-fm}\text{, }&m\neq 0\text{ and }n\neq 0\text{ and }z\neq \frac{fm}{3}\\b\neq 0\text{, }&z=\frac{fm}{3}\text{ and }n=0\text{ and }m\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$b\times 3z+mn=fbm$$

Tangohia te fbm mai i ngā taha e rua.

$$b\times 3z+mn-fbm=0$$

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

$$b\times 3z-fbm=-mn$$

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

$$\left(3z-fm\right)b=-mn$$

Whakawehea ngā taha e rua ki te 3z-mf.

$$\frac{\left(3z-fm\right)b}{3z-fm}=-\frac{mn}{3z-fm}$$

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

$$b=-\frac{mn}{3z-fm}$$

Tē taea kia ōrite te tāupe b ki 0.

$$b=-\frac{mn}{3z-fm}\text{, }b\neq 0$$

Whakaoti mō f

$$f=\frac{3bz+mn}{bm}$$

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

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$b\times 3z+mn=fbm$$

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

$$fbm=b\times 3z+mn$$

He hanga arowhānui tō te whārite.

$$bmf=3bz+mn$$

Whakawehea ngā taha e rua ki te bm.

$$\frac{bmf}{bm}=\frac{3bz+mn}{bm}$$

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

$$f=\frac{3bz+mn}{bm}$$

Whakawehe 3zb+nm ki te bm.

$$f=\frac{n}{b}+\frac{3z}{m}$$