Whakaoti i te 5/x+8/y=5

$$\frac { 5 } { x } + \frac { 8 } { y } = 5$$

Whakaoti mō x

$$x=-\frac{5y}{8-5y}$$

$$y\neq 0\text{ and }y\neq \frac{8}{5}$$

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. Me whakarea ngā taha e rua o te whārite ki te xy, arā, te tauraro pātahi he tino iti rawa te kitea o x,y.

$$y\times 5+x\times 8=5xy$$

Tangohia te 5xy mai i ngā taha e rua.

$$y\times 5+x\times 8-5xy=0$$

Tangohia te y\times 5 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x\times 8-5xy=-y\times 5$$

Whakareatia te -1 ki te 5, ka -5.

$$x\times 8-5xy=-5y$$

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

$$\left(8-5y\right)x=-5y$$

Whakawehea ngā taha e rua ki te 8-5y.

$$\frac{\left(8-5y\right)x}{8-5y}=-\frac{5y}{8-5y}$$

Mā te whakawehe ki te 8-5y ka wetekia te whakareanga ki te 8-5y.

$$x=-\frac{5y}{8-5y}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{5y}{8-5y}\text{, }x\neq 0$$

Whakaoti mō y

$$y=-\frac{8x}{5\left(1-x\right)}$$

$$x\neq 0\text{ and }x\neq 1$$

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 xy, arā, te tauraro pātahi he tino iti rawa te kitea o x,y.

$$y\times 5+x\times 8=5xy$$

Tangohia te 5xy mai i ngā taha e rua.

$$y\times 5+x\times 8-5xy=0$$

Tangohia te x\times 8 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$y\times 5-5xy=-x\times 8$$

Whakareatia te -1 ki te 8, ka -8.

$$y\times 5-5xy=-8x$$

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

$$\left(5-5x\right)y=-8x$$

Whakawehea ngā taha e rua ki te -5x+5.

$$\frac{\left(5-5x\right)y}{5-5x}=-\frac{8x}{5-5x}$$

Mā te whakawehe ki te -5x+5 ka wetekia te whakareanga ki te -5x+5.

$$y=-\frac{8x}{5-5x}$$

Whakawehe -8x ki te -5x+5.

$$y=-\frac{8x}{5\left(1-x\right)}$$

Tē taea kia ōrite te tāupe y ki 0.

$$y=-\frac{8x}{5\left(1-x\right)}\text{, }y\neq 0$$