Whakaoti i te 049-x^2/07-xtext{para}x=-13é

$$\frac { 049 - x ^ { 2 } } { 07 - x } \text { para } x = - 13 é$$

Whakaoti mō p (complex solution)

$$\left\{\begin{matrix}p=-\frac{13é}{rx\left(x+7\right)a^{2}}\text{, }&a\neq 0\text{ and }r\neq 0\text{ and }x\neq -7\text{ and }x\neq 0\text{ and }x\neq 7\\p\in \mathrm{C}\text{, }&\left(a=0\text{ or }r=0\text{ or }x=-7\text{ or }x=0\right)\text{ and }é=0\text{ and }x\neq 7\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te -x+7.

$$\left(49-x^{2}\right)parax=-13é\left(-x+7\right)$$

Whakareatia te a ki te a, ka a^{2}.

$$\left(49-x^{2}\right)pa^{2}rx=-13é\left(-x+7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 49-x^{2} ki te p.

$$\left(49p-x^{2}p\right)a^{2}rx=-13é\left(-x+7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 49p-x^{2}p ki te a^{2}.

$$\left(49pa^{2}-x^{2}pa^{2}\right)rx=-13é\left(-x+7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 49pa^{2}-x^{2}pa^{2} ki te r.

$$\left(49pa^{2}r-x^{2}pa^{2}r\right)x=-13é\left(-x+7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 49pa^{2}r-x^{2}pa^{2}r ki te x.

$$49pa^{2}rx-pa^{2}rx^{3}=-13é\left(-x+7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -13é ki te -x+7.

$$49pa^{2}rx-pa^{2}rx^{3}=13éx-91é$$

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

$$\left(49a^{2}rx-a^{2}rx^{3}\right)p=13éx-91é$$

He hanga arowhānui tō te whārite.

$$\left(49rxa^{2}-ra^{2}x^{3}\right)p=13xé-91é$$

Whakawehea ngā taha e rua ki te 49a^{2}rx-a^{2}rx^{3}.

$$\frac{\left(49rxa^{2}-ra^{2}x^{3}\right)p}{49rxa^{2}-ra^{2}x^{3}}=\frac{13é\left(x-7\right)}{49rxa^{2}-ra^{2}x^{3}}$$

Mā te whakawehe ki te 49a^{2}rx-a^{2}rx^{3} ka wetekia te whakareanga ki te 49a^{2}rx-a^{2}rx^{3}.

$$p=\frac{13é\left(x-7\right)}{49rxa^{2}-ra^{2}x^{3}}$$

Whakawehe 13é\left(-7+x\right) ki te 49a^{2}rx-a^{2}rx^{3}.

$$p=-\frac{13é}{rx\left(x+7\right)a^{2}}$$

Whakaoti mō p

$$\left\{\begin{matrix}p=-\frac{13é}{rx\left(x+7\right)a^{2}}\text{, }&a\neq 0\text{ and }r\neq 0\text{ and }x\neq 0\text{ and }|x|\neq 7\\p\in \mathrm{R}\text{, }&\left(a=0\text{ or }r=0\text{ or }x=-7\text{ or }x=0\right)\text{ and }é=0\text{ and }x\neq 7\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te -x+7.

$$\left(49-x^{2}\right)parax=-13é\left(-x+7\right)$$

Whakareatia te a ki te a, ka a^{2}.

$$\left(49-x^{2}\right)pa^{2}rx=-13é\left(-x+7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 49-x^{2} ki te p.

$$\left(49p-x^{2}p\right)a^{2}rx=-13é\left(-x+7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 49p-x^{2}p ki te a^{2}.

$$\left(49pa^{2}-x^{2}pa^{2}\right)rx=-13é\left(-x+7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 49pa^{2}-x^{2}pa^{2} ki te r.

$$\left(49pa^{2}r-x^{2}pa^{2}r\right)x=-13é\left(-x+7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 49pa^{2}r-x^{2}pa^{2}r ki te x.

$$49pa^{2}rx-pa^{2}rx^{3}=-13é\left(-x+7\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -13é ki te -x+7.

$$49pa^{2}rx-pa^{2}rx^{3}=13éx-91é$$

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

$$\left(49a^{2}rx-a^{2}rx^{3}\right)p=13éx-91é$$

He hanga arowhānui tō te whārite.

$$\left(49rxa^{2}-ra^{2}x^{3}\right)p=13xé-91é$$

Whakawehea ngā taha e rua ki te 49a^{2}rx-a^{2}rx^{3}.

$$\frac{\left(49rxa^{2}-ra^{2}x^{3}\right)p}{49rxa^{2}-ra^{2}x^{3}}=\frac{13é\left(x-7\right)}{49rxa^{2}-ra^{2}x^{3}}$$

Mā te whakawehe ki te 49a^{2}rx-a^{2}rx^{3} ka wetekia te whakareanga ki te 49a^{2}rx-a^{2}rx^{3}.

$$p=\frac{13é\left(x-7\right)}{49rxa^{2}-ra^{2}x^{3}}$$

Whakawehe 13é\left(-7+x\right) ki te 49a^{2}rx-a^{2}rx^{3}.

$$p=-\frac{13é}{rx\left(x+7\right)a^{2}}$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=-ip^{-\frac{1}{2}}r^{-\frac{1}{2}}x^{-\frac{1}{2}}\left(x+7\right)^{-\frac{1}{2}}\sqrt{13é}\text{; }a=ip^{-\frac{1}{2}}r^{-\frac{1}{2}}x^{-\frac{1}{2}}\left(x+7\right)^{-\frac{1}{2}}\sqrt{13é}\text{, }&x\neq 0\text{ and }r\neq 0\text{ and }p\neq 0\text{ and }x\neq -7\text{ and }x\neq 7\\a\in \mathrm{C}\text{, }&x\neq 7\text{ and }\left(r=0\text{ or }p=0\text{ or }x=-7\text{ or }x=0\right)\text{ and }é=0\end{matrix}\right.$$