Whakaoti i te x/a+y/b=1.x/b+y/a=1

$$\frac { x } { a } + \frac { y } { b } = 1 . \frac { x } { b } + \frac { y } { a } = 1$$

Whakaoti mō a

$$\left\{\begin{matrix}a=-\frac{bx}{y-b}\text{, }&b\neq 0\text{ and }x\neq 0\text{ and }y\neq b\\a\neq 0\text{, }&b=y\text{ and }x=0\text{ and }y\neq 0\end{matrix}\right.$$

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.

$$bx+ay=ab$$

Tangohia te ab mai i ngā taha e rua.

$$bx+ay-ab=0$$

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

$$ay-ab=-bx$$

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

$$\left(y-b\right)a=-bx$$

Whakawehea ngā taha e rua ki te y-b.

$$\frac{\left(y-b\right)a}{y-b}=-\frac{bx}{y-b}$$

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

$$a=-\frac{bx}{y-b}$$

Tē taea kia ōrite te tāupe a ki 0.

$$a=-\frac{bx}{y-b}\text{, }a\neq 0$$

Whakaoti mō b

$$\left\{\begin{matrix}b=-\frac{ay}{x-a}\text{, }&a\neq 0\text{ and }y\neq 0\text{ and }x\neq a\\b\neq 0\text{, }&a=x\text{ and }y=0\text{ and }x\neq 0\end{matrix}\right.$$

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

$$bx+ay=ab$$

Tangohia te ab mai i ngā taha e rua.

$$bx+ay-ab=0$$

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

$$bx-ab=-ay$$

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

$$\left(x-a\right)b=-ay$$

Whakawehea ngā taha e rua ki te x-a.

$$\frac{\left(x-a\right)b}{x-a}=-\frac{ay}{x-a}$$

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

$$b=-\frac{ay}{x-a}$$

Tē taea kia ōrite te tāupe b ki 0.

$$b=-\frac{ay}{x-a}\text{, }b\neq 0$$