Whakaoti i te 1/a+1/b=1/c

$$\frac { 1 } { a } + \frac { 1 } { b } = \frac { 1 } { c }$$

Whakaoti mō a

$$a=-\frac{bc}{c-b}$$

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

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 abc, arā, te tauraro pātahi he tino iti rawa te kitea o a,b,c.

$$bc+ac=ab$$

Tangohia te ab mai i ngā taha e rua.

$$bc+ac-ab=0$$

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

$$ac-ab=-bc$$

Whakaraupapatia anō ngā kīanga tau.

$$-ab+ac=-bc$$

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

$$\left(-b+c\right)a=-bc$$

He hanga arowhānui tō te whārite.

$$\left(c-b\right)a=-bc$$

Whakawehea ngā taha e rua ki te -b+c.

$$\frac{\left(c-b\right)a}{c-b}=-\frac{bc}{c-b}$$

Mā te whakawehe ki te -b+c ka wetekia te whakareanga ki te -b+c.

$$a=-\frac{bc}{c-b}$$

Tē taea kia ōrite te tāupe a ki 0.

$$a=-\frac{bc}{c-b}\text{, }a\neq 0$$

Whakaoti mō b

$$b=-\frac{ac}{c-a}$$

$$a\neq 0\text{ and }c\neq 0\text{ and }a\neq c$$

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 abc, arā, te tauraro pātahi he tino iti rawa te kitea o a,b,c.

$$bc+ac=ab$$

Tangohia te ab mai i ngā taha e rua.

$$bc+ac-ab=0$$

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

$$bc-ab=-ac$$

Whakaraupapatia anō ngā kīanga tau.

$$-ab+bc=-ac$$

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

$$\left(-a+c\right)b=-ac$$

He hanga arowhānui tō te whārite.

$$\left(c-a\right)b=-ac$$

Whakawehea ngā taha e rua ki te c-a.

$$\frac{\left(c-a\right)b}{c-a}=-\frac{ac}{c-a}$$

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

$$b=-\frac{ac}{c-a}$$

Tē taea kia ōrite te tāupe b ki 0.

$$b=-\frac{ac}{c-a}\text{, }b\neq 0$$