Whakaoti i te m/n+9=m-4/m+1

$$\frac { m } { n + 9 } = \frac { m - 4 } { m + 1 }$$

Whakaoti mō n

$$n=-\frac{m^{2}-8m+36}{4-m}$$

$$m\neq -1\text{ and }m\neq 0\text{ and }m\neq 4$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe n ki -9 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(m+1\right)\left(n+9\right), arā, te tauraro pātahi he tino iti rawa te kitea o n+9,m+1.

$$\left(m+1\right)m=\left(n+9\right)\left(m-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te m+1 ki te m.

$$m^{2}+m=\left(n+9\right)\left(m-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te n+9 ki te m-4.

$$m^{2}+m=nm-4n+9m-36$$

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

$$nm-4n+9m-36=m^{2}+m$$

Tangohia te 9m mai i ngā taha e rua.

$$nm-4n-36=m^{2}+m-9m$$

Pahekotia te m me -9m, ka -8m.

$$nm-4n-36=m^{2}-8m$$

Me tāpiri te 36 ki ngā taha e rua.

$$nm-4n=m^{2}-8m+36$$

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

$$\left(m-4\right)n=m^{2}-8m+36$$

Whakawehea ngā taha e rua ki te m-4.

$$\frac{\left(m-4\right)n}{m-4}=\frac{m^{2}-8m+36}{m-4}$$

Mā te whakawehe ki te m-4 ka wetekia te whakareanga ki te m-4.

$$n=\frac{m^{2}-8m+36}{m-4}$$

Tē taea kia ōrite te tāupe n ki -9.

$$n=\frac{m^{2}-8m+36}{m-4}\text{, }n\neq -9$$

Whakaoti mō m

$$m=\frac{\sqrt{n^{2}-80}+n+8}{2}$$

$$m=\frac{-\sqrt{n^{2}-80}+n+8}{2}\text{, }n\geq 4\sqrt{5}\text{ or }\left(n\neq -9\text{ and }n\leq -4\sqrt{5}\right)$$