Whakaoti i te varepsilon-x=(I-x)f/varepsilon

$$\varepsilon - x = ( I - x ) \frac { f } { \varepsilon }$$

Whakaoti mō I (complex solution)

$$\left\{\begin{matrix}I=\frac{fx-x\epsilon +\epsilon ^{2}}{f}\text{, }&f\neq 0\text{ and }\epsilon \neq 0\\I\in \mathrm{C}\text{, }&\epsilon =x\text{ and }f=0\text{ and }x\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te \epsilon .

$$\epsilon \epsilon -x\epsilon =\left(I-x\right)f$$

Whakareatia te \epsilon ki te \epsilon , ka \epsilon ^{2}.

$$\epsilon ^{2}-x\epsilon =\left(I-x\right)f$$

Whakamahia te āhuatanga tohatoha hei whakarea te I-x ki te f.

$$\epsilon ^{2}-x\epsilon =If-xf$$

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

$$If-xf=\epsilon ^{2}-x\epsilon$$

Me tāpiri te xf ki ngā taha e rua.

$$If=\epsilon ^{2}-x\epsilon +xf$$

He hanga arowhānui tō te whārite.

$$fI=fx-x\epsilon +\epsilon ^{2}$$

Whakawehea ngā taha e rua ki te f.

$$\frac{fI}{f}=\frac{fx-x\epsilon +\epsilon ^{2}}{f}$$

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

$$I=\frac{fx-x\epsilon +\epsilon ^{2}}{f}$$

Whakaoti mō f (complex solution)

$$\left\{\begin{matrix}f=\frac{\epsilon \left(\epsilon -x\right)}{I-x}\text{, }&x\neq I\text{ and }\epsilon \neq 0\\f\in \mathrm{C}\text{, }&\epsilon =I\text{ and }x=I\text{ and }I\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te \epsilon .

$$\epsilon \epsilon -x\epsilon =\left(I-x\right)f$$

Whakareatia te \epsilon ki te \epsilon , ka \epsilon ^{2}.

$$\epsilon ^{2}-x\epsilon =\left(I-x\right)f$$

Whakamahia te āhuatanga tohatoha hei whakarea te I-x ki te f.

$$\epsilon ^{2}-x\epsilon =If-xf$$

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

$$If-xf=\epsilon ^{2}-x\epsilon$$

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

$$\left(I-x\right)f=\epsilon ^{2}-x\epsilon$$

Whakawehea ngā taha e rua ki te I-x.

$$\frac{\left(I-x\right)f}{I-x}=\frac{\epsilon \left(\epsilon -x\right)}{I-x}$$

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

$$f=\frac{\epsilon \left(\epsilon -x\right)}{I-x}$$

Whakaoti mō I

$$\left\{\begin{matrix}I=\frac{fx-x\epsilon +\epsilon ^{2}}{f}\text{, }&f\neq 0\text{ and }\epsilon \neq 0\\I\in \mathrm{R}\text{, }&\epsilon =x\text{ and }f=0\text{ and }x\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te \epsilon .

$$\epsilon \epsilon -x\epsilon =\left(I-x\right)f$$

Whakareatia te \epsilon ki te \epsilon , ka \epsilon ^{2}.

$$\epsilon ^{2}-x\epsilon =\left(I-x\right)f$$

Whakamahia te āhuatanga tohatoha hei whakarea te I-x ki te f.

$$\epsilon ^{2}-x\epsilon =If-xf$$

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

$$If-xf=\epsilon ^{2}-x\epsilon$$

Me tāpiri te xf ki ngā taha e rua.

$$If=\epsilon ^{2}-x\epsilon +xf$$

He hanga arowhānui tō te whārite.

$$fI=fx-x\epsilon +\epsilon ^{2}$$

Whakawehea ngā taha e rua ki te f.

$$\frac{fI}{f}=\frac{fx-x\epsilon +\epsilon ^{2}}{f}$$

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

$$I=\frac{fx-x\epsilon +\epsilon ^{2}}{f}$$

Whakaoti mō f

$$\left\{\begin{matrix}f=\frac{\epsilon \left(\epsilon -x\right)}{I-x}\text{, }&x\neq I\text{ and }\epsilon \neq 0\\f\in \mathrm{R}\text{, }&\epsilon =I\text{ and }x=I\text{ and }I\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te \epsilon .

$$\epsilon \epsilon -x\epsilon =\left(I-x\right)f$$

Whakareatia te \epsilon ki te \epsilon , ka \epsilon ^{2}.

$$\epsilon ^{2}-x\epsilon =\left(I-x\right)f$$

Whakamahia te āhuatanga tohatoha hei whakarea te I-x ki te f.

$$\epsilon ^{2}-x\epsilon =If-xf$$

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

$$If-xf=\epsilon ^{2}-x\epsilon$$

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

$$\left(I-x\right)f=\epsilon ^{2}-x\epsilon$$

Whakawehea ngā taha e rua ki te I-x.

$$\frac{\left(I-x\right)f}{I-x}=\frac{\epsilon \left(\epsilon -x\right)}{I-x}$$

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

$$f=\frac{\epsilon \left(\epsilon -x\right)}{I-x}$$