Whakaoti i te m+5n=m-n/12m

$$m + 5 n = \frac { m - n } { 12 m }$$

Whakaoti mō n

$$n=-\frac{m\left(12m-1\right)}{60m+1}$$

$$m\neq -\frac{1}{60}\text{ and }m\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 12m.

$$12mm+5n\times 12m=m-n$$

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

$$12m^{2}+5n\times 12m=m-n$$

Whakareatia te 5 ki te 12, ka 60.

$$12m^{2}+60nm=m-n$$

Me tāpiri te n ki ngā taha e rua.

$$12m^{2}+60nm+n=m$$

Tangohia te 12m^{2} mai i ngā taha e rua.

$$60nm+n=m-12m^{2}$$

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

$$\left(60m+1\right)n=m-12m^{2}$$

Whakawehea ngā taha e rua ki te 60m+1.

$$\frac{\left(60m+1\right)n}{60m+1}=\frac{m\left(1-12m\right)}{60m+1}$$

Mā te whakawehe ki te 60m+1 ka wetekia te whakareanga ki te 60m+1.

$$n=\frac{m\left(1-12m\right)}{60m+1}$$

Whakaoti mō m

$$\left\{\begin{matrix}m=-\frac{\sqrt{3600n^{2}-168n+1}}{24}-\frac{5n}{2}+\frac{1}{24}\text{, }&n\geq \frac{\sqrt{6}}{150}+\frac{7}{300}\text{ or }\left(n\neq 0\text{ and }n\leq -\frac{\sqrt{6}}{150}+\frac{7}{300}\right)\\m=\frac{\sqrt{3600n^{2}-168n+1}}{24}-\frac{5n}{2}+\frac{1}{24}\text{, }&n\geq \frac{\sqrt{6}}{150}+\frac{7}{300}\text{ or }n\leq -\frac{\sqrt{6}}{150}+\frac{7}{300}\end{matrix}\right.$$