Whakaoti i te 90/57-x=4left(92/4+13/4right)

$$\frac{ 90 }{ 57-x } = 4 \left( 9 \frac{ 2 }{ 4 } +1 \frac{ 3 }{ 4 } \right)$$

Whakaoti mō x

$$x=55$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 57 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 4\left(x-57\right), arā, te tauraro pātahi he tino iti rawa te kitea o 57-x,4.

$$-4\times 90=4\left(\frac{9\times 4+2}{4}+\frac{1\times 4+3}{4}\right)\times 4\left(x-57\right)$$

Whakareatia te -4 ki te 90, ka -360.

$$-360=4\left(\frac{9\times 4+2}{4}+\frac{1\times 4+3}{4}\right)\times 4\left(x-57\right)$$

Whakareatia te 9 ki te 4, ka 36.

$$-360=4\left(\frac{36+2}{4}+\frac{1\times 4+3}{4}\right)\times 4\left(x-57\right)$$

Tāpirihia te 36 ki te 2, ka 38.

$$-360=4\left(\frac{38}{4}+\frac{1\times 4+3}{4}\right)\times 4\left(x-57\right)$$

Whakahekea te hautanga \frac{38}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$-360=4\left(\frac{19}{2}+\frac{1\times 4+3}{4}\right)\times 4\left(x-57\right)$$

Whakareatia te 1 ki te 4, ka 4.

$$-360=4\left(\frac{19}{2}+\frac{4+3}{4}\right)\times 4\left(x-57\right)$$

Tāpirihia te 4 ki te 3, ka 7.

$$-360=4\left(\frac{19}{2}+\frac{7}{4}\right)\times 4\left(x-57\right)$$

Tāpirihia te \frac{19}{2} ki te \frac{7}{4}, ka \frac{45}{4}.

$$-360=4\times \frac{45}{4}\times 4\left(x-57\right)$$

Whakareatia te 4 ki te \frac{45}{4}, ka 45.

$$-360=45\times 4\left(x-57\right)$$

Whakareatia te 45 ki te 4, ka 180.

$$-360=180\left(x-57\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 180 ki te x-57.

$$-360=180x-10260$$

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

$$180x-10260=-360$$

Me tāpiri te 10260 ki ngā taha e rua.

$$180x=-360+10260$$

Tāpirihia te -360 ki te 10260, ka 9900.

$$180x=9900$$

Whakawehea ngā taha e rua ki te 180.

$$x=\frac{9900}{180}$$

Whakawehea te 9900 ki te 180, kia riro ko 55.

$$x=55$$