Whakaoti i te 1/n+4/p=5/m

$$\frac { 1 } { n } + \frac { 4 } { p } = \frac { 5 } { m }$$

Whakaoti mō m

$$m=\frac{5np}{4n+p}$$

$$n\neq 0\text{ and }p\neq 0\text{ and }n\neq -\frac{p}{4}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$mp+mn\times 4=np\times 5$$

Whakaraupapatia anō ngā kīanga tau.

$$4mn+mp=5np$$

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

$$\left(4n+p\right)m=5np$$

Whakawehea ngā taha e rua ki te p+4n.

$$\frac{\left(4n+p\right)m}{4n+p}=\frac{5np}{4n+p}$$

Mā te whakawehe ki te p+4n ka wetekia te whakareanga ki te p+4n.

$$m=\frac{5np}{4n+p}$$

Tē taea kia ōrite te tāupe m ki 0.

$$m=\frac{5np}{4n+p}\text{, }m\neq 0$$

Whakaoti mō n

$$n=-\frac{mp}{4m-5p}$$

$$p\neq 0\text{ and }m\neq 0\text{ and }p\neq \frac{4m}{5}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$mp+mn\times 4=np\times 5$$

Tangohia te np\times 5 mai i ngā taha e rua.

$$mp+mn\times 4-np\times 5=0$$

Whakareatia te -1 ki te 5, ka -5.

$$mp+mn\times 4-5np=0$$

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

$$mn\times 4-5np=-mp$$

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

$$\left(m\times 4-5p\right)n=-mp$$

He hanga arowhānui tō te whārite.

$$\left(4m-5p\right)n=-mp$$

Whakawehea ngā taha e rua ki te 4m-5p.

$$\frac{\left(4m-5p\right)n}{4m-5p}=-\frac{mp}{4m-5p}$$

Mā te whakawehe ki te 4m-5p ka wetekia te whakareanga ki te 4m-5p.

$$n=-\frac{mp}{4m-5p}$$

Tē taea kia ōrite te tāupe n ki 0.

$$n=-\frac{mp}{4m-5p}\text{, }n\neq 0$$