Whakaoti i te 6/R-8=4(8Q+1)

$$\frac { 6 } { R - 8 } = 4 ( 8 Q + 1 )$$

Whakaoti mō Q

$$Q=-\frac{19-2R}{16\left(8-R\right)}$$

$$R\neq 8$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te R-8.

$$6=4\left(8Q+1\right)\left(R-8\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te 8Q+1.

$$6=\left(32Q+4\right)\left(R-8\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 32Q+4 ki te R-8.

$$6=32QR-256Q+4R-32$$

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

$$32QR-256Q+4R-32=6$$

Tangohia te 4R mai i ngā taha e rua.

$$32QR-256Q-32=6-4R$$

Me tāpiri te 32 ki ngā taha e rua.

$$32QR-256Q=6-4R+32$$

Tāpirihia te 6 ki te 32, ka 38.

$$32QR-256Q=38-4R$$

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

$$\left(32R-256\right)Q=38-4R$$

Whakawehea ngā taha e rua ki te 32R-256.

$$\frac{\left(32R-256\right)Q}{32R-256}=\frac{38-4R}{32R-256}$$

Mā te whakawehe ki te 32R-256 ka wetekia te whakareanga ki te 32R-256.

$$Q=\frac{38-4R}{32R-256}$$

Whakawehe 38-4R ki te 32R-256.

$$Q=\frac{19-2R}{16\left(R-8\right)}$$

Whakaoti mō R

$$R=\frac{128Q+19}{2\left(8Q+1\right)}$$

$$Q\neq -\frac{1}{8}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe R ki 8 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te R-8.

$$6=4\left(8Q+1\right)\left(R-8\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te 8Q+1.

$$6=\left(32Q+4\right)\left(R-8\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 32Q+4 ki te R-8.

$$6=32QR-256Q+4R-32$$

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

$$32QR-256Q+4R-32=6$$

Me tāpiri te 256Q ki ngā taha e rua.

$$32QR+4R-32=6+256Q$$

Me tāpiri te 32 ki ngā taha e rua.

$$32QR+4R=6+256Q+32$$

Tāpirihia te 6 ki te 32, ka 38.

$$32QR+4R=38+256Q$$

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

$$\left(32Q+4\right)R=38+256Q$$

He hanga arowhānui tō te whārite.

$$\left(32Q+4\right)R=256Q+38$$

Whakawehea ngā taha e rua ki te 32Q+4.

$$\frac{\left(32Q+4\right)R}{32Q+4}=\frac{256Q+38}{32Q+4}$$

Mā te whakawehe ki te 32Q+4 ka wetekia te whakareanga ki te 32Q+4.

$$R=\frac{256Q+38}{32Q+4}$$

Whakawehe 38+256Q ki te 32Q+4.

$$R=\frac{128Q+19}{2\left(8Q+1\right)}$$

Tē taea kia ōrite te tāupe R ki 8.

$$R=\frac{128Q+19}{2\left(8Q+1\right)}\text{, }R\neq 8$$