Whakaoti i te t_{1}=D/c-v+D/c+v=

$$t _ { 1 } = \frac { D } { c - v } + \frac { D } { c + v } =$$

Whakaoti mō D

$$\left\{\begin{matrix}D=\frac{t_{1}\left(c^{2}-v^{2}\right)}{2c}\text{, }&c\neq 0\text{ and }|c|\neq |v|\\D\in \mathrm{R}\text{, }&t_{1}=0\text{ and }c=0\text{ and }v\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te \left(-v+c\right)\left(-v-c\right), arā, te tauraro pātahi he tino iti rawa te kitea o c-v,c+v.

$$t_{1}\left(-v+c\right)\left(-v-c\right)=\left(-v-c\right)D+\left(-c+v\right)D$$

Whakamahia te āhuatanga tohatoha hei whakarea te t_{1} ki te -v+c.

$$\left(-t_{1}v+t_{1}c\right)\left(-v-c\right)=\left(-v-c\right)D+\left(-c+v\right)D$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -t_{1}v+t_{1}c ki te -v-c ka whakakotahi i ngā kupu rite.

$$v^{2}t_{1}-t_{1}c^{2}=\left(-v-c\right)D+\left(-c+v\right)D$$

Whakamahia te āhuatanga tohatoha hei whakarea te -v-c ki te D.

$$v^{2}t_{1}-t_{1}c^{2}=-vD-cD+\left(-c+v\right)D$$

Whakamahia te āhuatanga tohatoha hei whakarea te -c+v ki te D.

$$v^{2}t_{1}-t_{1}c^{2}=-vD-cD-cD+vD$$

Pahekotia te -cD me -cD, ka -2cD.

$$v^{2}t_{1}-t_{1}c^{2}=-vD-2cD+vD$$

Pahekotia te -vD me vD, ka 0.

$$v^{2}t_{1}-t_{1}c^{2}=-2cD$$

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

$$-2cD=v^{2}t_{1}-t_{1}c^{2}$$

He hanga arowhānui tō te whārite.

$$\left(-2c\right)D=t_{1}v^{2}-t_{1}c^{2}$$

Whakawehea ngā taha e rua ki te -2c.

$$\frac{\left(-2c\right)D}{-2c}=\frac{t_{1}\left(v-c\right)\left(v+c\right)}{-2c}$$

Mā te whakawehe ki te -2c ka wetekia te whakareanga ki te -2c.

$$D=\frac{t_{1}\left(v-c\right)\left(v+c\right)}{-2c}$$

Whakawehe t_{1}\left(v-c\right)\left(v+c\right) ki te -2c.

$$D=-\frac{t_{1}\left(v-c\right)\left(v+c\right)}{2c}$$

Whakaoti mō c

$$\left\{\begin{matrix}c=\frac{\sqrt{\left(t_{1}v\right)^{2}+D^{2}}+D}{t_{1}}\text{; }c=\frac{-\sqrt{\left(t_{1}v\right)^{2}+D^{2}}+D}{t_{1}}\text{, }&v\neq 0\text{ and }D\neq 0\text{ and }t_{1}\neq 0\\c=0\text{, }&v\neq 0\text{ and }t_{1}=0\text{ and }D\neq 0\\c\in \mathrm{R}\setminus v,-v\text{, }&t_{1}=0\text{ and }D=0\end{matrix}\right.$$