Whakaoti i te (a^3+8):(a^2-4)=x:(a-2)

$$( a ^ { 3 } + 8 ) : ( a ^ { 2 } - 4 ) = x : ( a - 2 )$$

Whakaoti mō x (complex solution)

$$x=a^{2}-2a+4$$

$$a\neq -2\text{ and }a\neq 2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te \left(a-2\right)\left(a+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o a^{2}-4,a-2.

$$a^{3}+8=\left(a+2\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te a+2 ki te x.

$$a^{3}+8=ax+2x$$

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

$$ax+2x=a^{3}+8$$

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

$$\left(a+2\right)x=a^{3}+8$$

Whakawehea ngā taha e rua ki te a+2.

$$\frac{\left(a+2\right)x}{a+2}=\frac{a^{3}+8}{a+2}$$

Mā te whakawehe ki te a+2 ka wetekia te whakareanga ki te a+2.

$$x=\frac{a^{3}+8}{a+2}$$

Whakawehe a^{3}+8 ki te a+2.

$$x=a^{2}-2a+4$$

Whakaoti mō x

$$x=a^{2}-2a+4$$

$$|a|\neq 2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te \left(a-2\right)\left(a+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o a^{2}-4,a-2.

$$a^{3}+8=\left(a+2\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te a+2 ki te x.

$$a^{3}+8=ax+2x$$

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

$$ax+2x=a^{3}+8$$

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

$$\left(a+2\right)x=a^{3}+8$$

Whakawehea ngā taha e rua ki te a+2.

$$\frac{\left(a+2\right)x}{a+2}=\frac{a^{3}+8}{a+2}$$

Mā te whakawehe ki te a+2 ka wetekia te whakareanga ki te a+2.

$$x=\frac{a^{3}+8}{a+2}$$

Whakawehe a^{3}+8 ki te a+2.

$$x=a^{2}-2a+4$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=-\sqrt{x-3}+1\text{, }&x\neq 12\\a=\sqrt{x-3}+1\text{, }&x\neq 4\end{matrix}\right.$$

Whakaoti mō a

$$\left\{\begin{matrix}a=-\sqrt{x-3}+1\text{, }&x\geq 3\text{ and }x\neq 12\\a=\sqrt{x-3}+1\text{, }&x\neq 4\text{ and }x\geq 3\end{matrix}\right.$$