Whakaoti i te 2/x-1/frac{1-frac{1{10}}{10/x}}=2/x

$$\frac { \frac { 2 } { x - 1 } } { \frac { 1 - \frac { 1 } { 10 } } { \frac { 10 } { x } } } = \frac { 2 } { x }$$

Whakaoti mō x

$$x = \frac{109}{9} = 12\frac{1}{9} \approx 12.111111111$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$\frac{100}{9}\times \frac{2}{x-1}=2$$

Me whakarea te \frac{100}{9} ki te \frac{2}{x-1} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{100\times 2}{9\left(x-1\right)}=2$$

Whakareatia te 100 ki te 2, ka 200.

$$\frac{200}{9\left(x-1\right)}=2$$

Tē taea kia ōrite te tāupe x ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 9\left(x-1\right).

$$200=18\left(x-1\right)$$

Whakawehea ngā taha e rua ki te 18.

$$\frac{200}{18}=x-1$$

Whakahekea te hautanga \frac{200}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{100}{9}=x-1$$

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

$$x-1=\frac{100}{9}$$

Me tāpiri te 1 ki ngā taha e rua.

$$x=\frac{100}{9}+1$$

Tāpirihia te \frac{100}{9} ki te 1, ka \frac{109}{9}.

$$x=\frac{109}{9}$$