Whakaoti i te 8-02dt/1+t=175dθ

$$\frac { 8 - 02 d t } { 1 + t } = 175 d \theta$$

Whakaoti mō d

$$d=\frac{8}{175t\theta +2t+175\theta }$$

$$\left(\theta =-\frac{2}{175}\text{ or }t\neq -\frac{175\theta }{175\theta +2}\right)\text{ and }t\neq -1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te t+1.

$$8-2dt=175d\theta \left(t+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 175d\theta ki te t+1.

$$8-2dt=175d\theta t+175d\theta$$

Tangohia te 175d\theta t mai i ngā taha e rua.

$$8-2dt-175d\theta t=175d\theta$$

Tangohia te 175d\theta mai i ngā taha e rua.

$$8-2dt-175d\theta t-175d\theta =0$$

Tangohia te 8 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-2dt-175d\theta t-175d\theta =-8$$

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

$$\left(-2t-175\theta t-175\theta \right)d=-8$$

He hanga arowhānui tō te whārite.

$$\left(-175t\theta -2t-175\theta \right)d=-8$$

Whakawehea ngā taha e rua ki te -175t\theta -2t-175\theta .

$$\frac{\left(-175t\theta -2t-175\theta \right)d}{-175t\theta -2t-175\theta }=-\frac{8}{-175t\theta -2t-175\theta }$$

Mā te whakawehe ki te -175t\theta -2t-175\theta ka wetekia te whakareanga ki te -175t\theta -2t-175\theta .

$$d=-\frac{8}{-175t\theta -2t-175\theta }$$

Whakawehe -8 ki te -175t\theta -2t-175\theta .

$$d=\frac{8}{175t\theta +2t+175\theta }$$

Whakaoti mō t

$$\left\{\begin{matrix}t=\frac{8-175d\theta }{d\left(175\theta +2\right)}\text{, }&d\neq -4\text{ and }\theta \neq -\frac{2}{175}\text{ and }d\neq 0\\t\neq -1\text{, }&\theta =-\frac{2}{175}\text{ and }d=-4\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe t ki -1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te t+1.

$$8-2dt=175d\theta \left(t+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 175d\theta ki te t+1.

$$8-2dt=175d\theta t+175d\theta$$

Tangohia te 175d\theta t mai i ngā taha e rua.

$$8-2dt-175d\theta t=175d\theta$$

Tangohia te 8 mai i ngā taha e rua.

$$-2dt-175d\theta t=175d\theta -8$$

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

$$\left(-2d-175d\theta \right)t=175d\theta -8$$

He hanga arowhānui tō te whārite.

$$\left(-175d\theta -2d\right)t=175d\theta -8$$

Whakawehea ngā taha e rua ki te -2d-175\theta d.

$$\frac{\left(-175d\theta -2d\right)t}{-175d\theta -2d}=\frac{175d\theta -8}{-175d\theta -2d}$$

Mā te whakawehe ki te -2d-175\theta d ka wetekia te whakareanga ki te -2d-175\theta d.

$$t=\frac{175d\theta -8}{-175d\theta -2d}$$

Whakawehe 175d\theta -8 ki te -2d-175\theta d.

$$t=\frac{175d\theta -8}{-d\left(175\theta +2\right)}$$

Tē taea kia ōrite te tāupe t ki -1.

$$t=\frac{175d\theta -8}{-d\left(175\theta +2\right)}\text{, }t\neq -1$$