Whakaoti i te Pa(p-q)+d(p+q)(p-q)-d(p+q)=0

$$P a ( p - q ) + d ( p + q ) ( p - q ) - d ( p + q ) = 0$$

Whakaoti mō P

$$\left\{\begin{matrix}P=-\frac{d\left(p-q-1\right)\left(p+q\right)}{a\left(p-q\right)}\text{, }&p\neq q\text{ and }a\neq 0\\P\in \mathrm{R}\text{, }&\left(d=0\text{ and }p=q\right)\text{ or }\left(p=0\text{ and }q=0\right)\text{ or }\left(a=0\text{ and }p=q+1\right)\text{ or }\left(p=-q\text{ and }a=0\text{ and }q\neq 0\right)\text{ or }\left(d=0\text{ and }a=0\text{ and }p\neq q\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te Pa ki te p-q.

$$Pap-Paq+d\left(p+q\right)\left(p-q\right)-d\left(p+q\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te d ki te p+q.

$$Pap-Paq+\left(dp+dq\right)\left(p-q\right)-d\left(p+q\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te dp+dq ki te p-q ka whakakotahi i ngā kupu rite.

$$Pap-Paq+dp^{2}-dq^{2}-d\left(p+q\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te d ki te p+q.

$$Pap-Paq+dp^{2}-dq^{2}-\left(dp+dq\right)=0$$

Hei kimi i te tauaro o dp+dq, kimihia te tauaro o ia taurangi.

$$Pap-Paq+dp^{2}-dq^{2}-dp-dq=0$$

Tangohia te dp^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$Pap-Paq-dq^{2}-dp-dq=-dp^{2}$$

Me tāpiri te dq^{2} ki ngā taha e rua.

$$Pap-Paq-dp-dq=-dp^{2}+dq^{2}$$

Me tāpiri te dp ki ngā taha e rua.

$$Pap-Paq-dq=-dp^{2}+dq^{2}+dp$$

Me tāpiri te dq ki ngā taha e rua.

$$Pap-Paq=-dp^{2}+dq^{2}+dp+dq$$

Whakaraupapatia anō ngā kīanga tau.

$$Pap-Paq=-dp^{2}+dp+dq^{2}+dq$$

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

$$\left(ap-aq\right)P=-dp^{2}+dp+dq^{2}+dq$$

He hanga arowhānui tō te whārite.

$$\left(ap-aq\right)P=dq+dq^{2}+dp-dp^{2}$$

Whakawehea ngā taha e rua ki te ap-aq.

$$\frac{\left(ap-aq\right)P}{ap-aq}=-\frac{d\left(p-q-1\right)\left(p+q\right)}{ap-aq}$$

Mā te whakawehe ki te ap-aq ka wetekia te whakareanga ki te ap-aq.

$$P=-\frac{d\left(p-q-1\right)\left(p+q\right)}{ap-aq}$$

Whakawehe -d\left(-1+p-q\right)\left(p+q\right) ki te ap-aq.

$$P=-\frac{d\left(p-q-1\right)\left(p+q\right)}{a\left(p-q\right)}$$

Whakaoti mō a

$$\left\{\begin{matrix}a=-\frac{d\left(p-q-1\right)\left(p+q\right)}{P\left(p-q\right)}\text{, }&p\neq q\text{ and }P\neq 0\\a\in \mathrm{R}\text{, }&\left(d=0\text{ and }p=q\right)\text{ or }\left(p=0\text{ and }q=0\right)\text{ or }\left(P=0\text{ and }p=q+1\right)\text{ or }\left(p=-q\text{ and }P=0\text{ and }q\neq 0\right)\text{ or }\left(d=0\text{ and }P=0\text{ and }p\neq q\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te Pa ki te p-q.

$$Pap-Paq+d\left(p+q\right)\left(p-q\right)-d\left(p+q\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te d ki te p+q.

$$Pap-Paq+\left(dp+dq\right)\left(p-q\right)-d\left(p+q\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te dp+dq ki te p-q ka whakakotahi i ngā kupu rite.

$$Pap-Paq+dp^{2}-dq^{2}-d\left(p+q\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te d ki te p+q.

$$Pap-Paq+dp^{2}-dq^{2}-\left(dp+dq\right)=0$$

Hei kimi i te tauaro o dp+dq, kimihia te tauaro o ia taurangi.

$$Pap-Paq+dp^{2}-dq^{2}-dp-dq=0$$

Tangohia te dp^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$Pap-Paq-dq^{2}-dp-dq=-dp^{2}$$

Me tāpiri te dq^{2} ki ngā taha e rua.

$$Pap-Paq-dp-dq=-dp^{2}+dq^{2}$$

Me tāpiri te dp ki ngā taha e rua.

$$Pap-Paq-dq=-dp^{2}+dq^{2}+dp$$

Me tāpiri te dq ki ngā taha e rua.

$$Pap-Paq=-dp^{2}+dq^{2}+dp+dq$$

Whakaraupapatia anō ngā kīanga tau.

$$Pap-Paq=-dp^{2}+dp+dq^{2}+dq$$

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

$$\left(Pp-Pq\right)a=-dp^{2}+dp+dq^{2}+dq$$

He hanga arowhānui tō te whārite.

$$\left(Pp-Pq\right)a=dq+dq^{2}+dp-dp^{2}$$

Whakawehea ngā taha e rua ki te Pp-Pq.

$$\frac{\left(Pp-Pq\right)a}{Pp-Pq}=-\frac{d\left(p-q-1\right)\left(p+q\right)}{Pp-Pq}$$

Mā te whakawehe ki te Pp-Pq ka wetekia te whakareanga ki te Pp-Pq.

$$a=-\frac{d\left(p-q-1\right)\left(p+q\right)}{Pp-Pq}$$

Whakawehe -d\left(-1+p-q\right)\left(p+q\right) ki te Pp-Pq.

$$a=-\frac{d\left(p-q-1\right)\left(p+q\right)}{P\left(p-q\right)}$$