Whakaoti i te y=5x+1/2x-4

$$y = \frac { 5 x + 1 } { 2 x - 4 }$$

Whakaoti mō x

$$x=\frac{4y+1}{2y-5}$$

$$y\neq \frac{5}{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 2 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 2\left(x-2\right).

$$y\times 2\left(x-2\right)=5x+1$$

Whakamahia te āhuatanga tohatoha hei whakarea te y\times 2 ki te x-2.

$$2yx-2y\times 2=5x+1$$

Whakareatia te -2 ki te 2, ka -4.

$$2yx-4y=5x+1$$

Tangohia te 5x mai i ngā taha e rua.

$$2yx-4y-5x=1$$

Me tāpiri te 4y ki ngā taha e rua.

$$2yx-5x=1+4y$$

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

$$\left(2y-5\right)x=1+4y$$

He hanga arowhānui tō te whārite.

$$\left(2y-5\right)x=4y+1$$

Whakawehea ngā taha e rua ki te 2y-5.

$$\frac{\left(2y-5\right)x}{2y-5}=\frac{4y+1}{2y-5}$$

Mā te whakawehe ki te 2y-5 ka wetekia te whakareanga ki te 2y-5.

$$x=\frac{4y+1}{2y-5}$$

Tē taea kia ōrite te tāupe x ki 2.

$$x=\frac{4y+1}{2y-5}\text{, }x\neq 2$$

Whakaoti mō y

$$y=\frac{5x+1}{2\left(x-2\right)}$$

$$x\neq 2$$