Whakaoti i te 3b/2y+3-b-y/x-5=1

$$\frac { 3 b } { 2 y + 3 } - \frac { b - y } { x - 5 } = 1$$

Whakaoti mō b (complex solution)

$$\left\{\begin{matrix}b=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}\text{, }&y\neq \frac{3x}{2}-9\text{ and }y\neq -\frac{3}{2}\text{ and }x\neq 5\\b\in \mathrm{C}\text{, }&y=3\text{ and }x=8\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te \left(x-5\right)\left(2y+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2y+3,x-5.

$$\left(x-5\right)\times 3b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-5 ki te 3.

$$\left(3x-15\right)b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x-15 ki te b.

$$3xb-15b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2y+3 ki te b-y.

$$3xb-15b-\left(2yb-2y^{2}+3b-3y\right)=\left(x-5\right)\left(2y+3\right)$$

Hei kimi i te tauaro o 2yb-2y^{2}+3b-3y, kimihia te tauaro o ia taurangi.

$$3xb-15b-2yb+2y^{2}-3b+3y=\left(x-5\right)\left(2y+3\right)$$

Pahekotia te -15b me -3b, ka -18b.

$$3xb-18b-2yb+2y^{2}+3y=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-5 ki te 2y+3.

$$3xb-18b-2yb+2y^{2}+3y=2xy+3x-10y-15$$

Tangohia te 2y^{2} mai i ngā taha e rua.

$$3xb-18b-2yb+3y=2xy+3x-10y-15-2y^{2}$$

Tangohia te 3y mai i ngā taha e rua.

$$3xb-18b-2yb=2xy+3x-10y-15-2y^{2}-3y$$

Pahekotia te -10y me -3y, ka -13y.

$$3xb-18b-2yb=2xy+3x-13y-15-2y^{2}$$

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

$$\left(3x-18-2y\right)b=2xy+3x-13y-15-2y^{2}$$

He hanga arowhānui tō te whārite.

$$\left(3x-2y-18\right)b=2xy+3x-2y^{2}-13y-15$$

Whakawehea ngā taha e rua ki te 3x-2y-18.

$$\frac{\left(3x-2y-18\right)b}{3x-2y-18}=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}$$

Mā te whakawehe ki te 3x-2y-18 ka wetekia te whakareanga ki te 3x-2y-18.

$$b=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}$$

Whakaoti mō b

$$\left\{\begin{matrix}b=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}\text{, }&y\neq \frac{3x}{2}-9\text{ and }y\neq -\frac{3}{2}\text{ and }x\neq 5\\b\in \mathrm{R}\text{, }&y=3\text{ and }x=8\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te \left(x-5\right)\left(2y+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2y+3,x-5.

$$\left(x-5\right)\times 3b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-5 ki te 3.

$$\left(3x-15\right)b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x-15 ki te b.

$$3xb-15b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2y+3 ki te b-y.

$$3xb-15b-\left(2yb-2y^{2}+3b-3y\right)=\left(x-5\right)\left(2y+3\right)$$

Hei kimi i te tauaro o 2yb-2y^{2}+3b-3y, kimihia te tauaro o ia taurangi.

$$3xb-15b-2yb+2y^{2}-3b+3y=\left(x-5\right)\left(2y+3\right)$$

Pahekotia te -15b me -3b, ka -18b.

$$3xb-18b-2yb+2y^{2}+3y=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-5 ki te 2y+3.

$$3xb-18b-2yb+2y^{2}+3y=2xy+3x-10y-15$$

Tangohia te 2y^{2} mai i ngā taha e rua.

$$3xb-18b-2yb+3y=2xy+3x-10y-15-2y^{2}$$

Tangohia te 3y mai i ngā taha e rua.

$$3xb-18b-2yb=2xy+3x-10y-15-2y^{2}-3y$$

Pahekotia te -10y me -3y, ka -13y.

$$3xb-18b-2yb=2xy+3x-13y-15-2y^{2}$$

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

$$\left(3x-18-2y\right)b=2xy+3x-13y-15-2y^{2}$$

He hanga arowhānui tō te whārite.

$$\left(3x-2y-18\right)b=2xy+3x-2y^{2}-13y-15$$

Whakawehea ngā taha e rua ki te 3x-2y-18.

$$\frac{\left(3x-2y-18\right)b}{3x-2y-18}=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}$$

Mā te whakawehe ki te 3x-2y-18 ka wetekia te whakareanga ki te 3x-2y-18.

$$b=\frac{\left(x-y-5\right)\left(2y+3\right)}{3x-2y-18}$$

Whakaoti mō x

$$\left\{\begin{matrix}x=-\frac{2y^{2}-2by+13y-18b+15}{-2y+3b-3}\text{, }&y\neq -\frac{3}{2}\text{ and }b\neq y\text{ and }b\neq \frac{2y}{3}+1\\x\neq 5\text{, }&y=3\text{ and }b=3\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 5 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-5\right)\left(2y+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2y+3,x-5.

$$\left(x-5\right)\times 3b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-5 ki te 3.

$$\left(3x-15\right)b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x-15 ki te b.

$$3xb-15b-\left(2y+3\right)\left(b-y\right)=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2y+3 ki te b-y.

$$3xb-15b-\left(2yb-2y^{2}+3b-3y\right)=\left(x-5\right)\left(2y+3\right)$$

Hei kimi i te tauaro o 2yb-2y^{2}+3b-3y, kimihia te tauaro o ia taurangi.

$$3xb-15b-2yb+2y^{2}-3b+3y=\left(x-5\right)\left(2y+3\right)$$

Pahekotia te -15b me -3b, ka -18b.

$$3xb-18b-2yb+2y^{2}+3y=\left(x-5\right)\left(2y+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-5 ki te 2y+3.

$$3xb-18b-2yb+2y^{2}+3y=2xy+3x-10y-15$$

Tangohia te 2xy mai i ngā taha e rua.

$$3xb-18b-2yb+2y^{2}+3y-2xy=3x-10y-15$$

Tangohia te 3x mai i ngā taha e rua.

$$3xb-18b-2yb+2y^{2}+3y-2xy-3x=-10y-15$$

Me tāpiri te 18b ki ngā taha e rua.

$$3xb-2yb+2y^{2}+3y-2xy-3x=-10y-15+18b$$

Me tāpiri te 2yb ki ngā taha e rua.

$$3xb+2y^{2}+3y-2xy-3x=-10y-15+18b+2yb$$

Tangohia te 2y^{2} mai i ngā taha e rua.

$$3xb+3y-2xy-3x=-10y-15+18b+2yb-2y^{2}$$

Tangohia te 3y mai i ngā taha e rua.

$$3xb-2xy-3x=-10y-15+18b+2yb-2y^{2}-3y$$

Pahekotia te -10y me -3y, ka -13y.

$$3xb-2xy-3x=-13y-15+18b+2yb-2y^{2}$$

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

$$\left(3b-2y-3\right)x=-13y-15+18b+2yb-2y^{2}$$

He hanga arowhānui tō te whārite.

$$\left(-2y+3b-3\right)x=-2y^{2}+2by-13y+18b-15$$

Whakawehea ngā taha e rua ki te -2y+3b-3.

$$\frac{\left(-2y+3b-3\right)x}{-2y+3b-3}=\frac{-2y^{2}+2by-13y+18b-15}{-2y+3b-3}$$

Mā te whakawehe ki te -2y+3b-3 ka wetekia te whakareanga ki te -2y+3b-3.

$$x=\frac{-2y^{2}+2by-13y+18b-15}{-2y+3b-3}$$

Tē taea kia ōrite te tāupe x ki 5.

$$x=\frac{-2y^{2}+2by-13y+18b-15}{-2y+3b-3}\text{, }x\neq 5$$