Whakaoti i te (x-4)/(-3x+1)=14/y

$$\frac { ( x - 4 ) } { ( - 3 x + 1 ) } = \frac { 14 } { y }$$

Whakaoti mō x

$$x=\frac{2\left(2y+7\right)}{y+42}$$

$$y\neq 0\text{ and }y\neq -42$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki \frac{1}{3} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te y\left(3x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o -3x+1,y.

$$-y\left(x-4\right)=\left(3x-1\right)\times 14$$

Whakamahia te āhuatanga tohatoha hei whakarea te -y ki te x-4.

$$-yx+4y=\left(3x-1\right)\times 14$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x-1 ki te 14.

$$-yx+4y=42x-14$$

Tangohia te 42x mai i ngā taha e rua.

$$-yx+4y-42x=-14$$

Tangohia te 4y mai i ngā taha e rua.

$$-yx-42x=-14-4y$$

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

$$\left(-y-42\right)x=-14-4y$$

He hanga arowhānui tō te whārite.

$$\left(-y-42\right)x=-4y-14$$

Whakawehea ngā taha e rua ki te -y-42.

$$\frac{\left(-y-42\right)x}{-y-42}=\frac{-4y-14}{-y-42}$$

Mā te whakawehe ki te -y-42 ka wetekia te whakareanga ki te -y-42.

$$x=\frac{-4y-14}{-y-42}$$

Whakawehe -4y-14 ki te -y-42.

$$x=\frac{2\left(2y+7\right)}{y+42}$$

Tē taea kia ōrite te tāupe x ki \frac{1}{3}.

$$x=\frac{2\left(2y+7\right)}{y+42}\text{, }x\neq \frac{1}{3}$$

Whakaoti mō y

$$y=-\frac{14\left(3x-1\right)}{x-4}$$

$$x\neq \frac{1}{3}\text{ and }x\neq 4$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe y ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te y\left(3x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o -3x+1,y.

$$-y\left(x-4\right)=\left(3x-1\right)\times 14$$

Whakamahia te āhuatanga tohatoha hei whakarea te -y ki te x-4.

$$-yx+4y=\left(3x-1\right)\times 14$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x-1 ki te 14.

$$-yx+4y=42x-14$$

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

$$\left(-x+4\right)y=42x-14$$

He hanga arowhānui tō te whārite.

$$\left(4-x\right)y=42x-14$$

Whakawehea ngā taha e rua ki te -x+4.

$$\frac{\left(4-x\right)y}{4-x}=\frac{42x-14}{4-x}$$

Mā te whakawehe ki te -x+4 ka wetekia te whakareanga ki te -x+4.

$$y=\frac{42x-14}{4-x}$$

Whakawehe 42x-14 ki te -x+4.

$$y=\frac{14\left(3x-1\right)}{4-x}$$

Tē taea kia ōrite te tāupe y ki 0.

$$y=\frac{14\left(3x-1\right)}{4-x}\text{, }y\neq 0$$