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

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

Whakaoti mō b

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

$$x\neq 18\text{ and }x\neq -\frac{3}{2}\text{ and }x\neq 5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

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

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

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

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

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

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

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

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

Pahekotia te 3xb me -2xb, ka xb.

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

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

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

Whakamahia te āhuatanga tuaritanga hei whakarea te x-5 ki te 2x+3 ka whakakotahi i ngā kupu rite.

$$xb-18b+2x^{2}+3x=2x^{2}-7x-15$$

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

$$xb-18b+3x=2x^{2}-7x-15-2x^{2}$$

Pahekotia te 2x^{2} me -2x^{2}, ka 0.

$$xb-18b+3x=-7x-15$$

Tangohia te 3x mai i ngā taha e rua.

$$xb-18b=-7x-15-3x$$

Pahekotia te -7x me -3x, ka -10x.

$$xb-18b=-10x-15$$

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

$$\left(x-18\right)b=-10x-15$$

Whakawehea ngā taha e rua ki te x-18.

$$\frac{\left(x-18\right)b}{x-18}=\frac{-10x-15}{x-18}$$

Mā te whakawehe ki te x-18 ka wetekia te whakareanga ki te x-18.

$$b=\frac{-10x-15}{x-18}$$

Whakawehe -10x-15 ki te x-18.

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

Whakaoti mō x

$$x=-\frac{3\left(5-6b\right)}{b+10}$$

$$b\neq 0\text{ and }b\neq -10\text{ and }b\neq 5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{3}{2},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(2x+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x+3,x-5.

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

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

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

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

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

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

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

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

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

Pahekotia te 3xb me -2xb, ka xb.

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

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

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

Whakamahia te āhuatanga tuaritanga hei whakarea te x-5 ki te 2x+3 ka whakakotahi i ngā kupu rite.

$$xb-18b+2x^{2}+3x=2x^{2}-7x-15$$

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

$$xb-18b+2x^{2}+3x-2x^{2}=-7x-15$$

Pahekotia te 2x^{2} me -2x^{2}, ka 0.

$$xb-18b+3x=-7x-15$$

Me tāpiri te 7x ki ngā taha e rua.

$$xb-18b+3x+7x=-15$$

Pahekotia te 3x me 7x, ka 10x.

$$xb-18b+10x=-15$$

Me tāpiri te 18b ki ngā taha e rua.

$$xb+10x=-15+18b$$

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

$$\left(b+10\right)x=-15+18b$$

He hanga arowhānui tō te whārite.

$$\left(b+10\right)x=18b-15$$

Whakawehea ngā taha e rua ki te b+10.

$$\frac{\left(b+10\right)x}{b+10}=\frac{18b-15}{b+10}$$

Mā te whakawehe ki te b+10 ka wetekia te whakareanga ki te b+10.

$$x=\frac{18b-15}{b+10}$$

Whakawehe -15+18b ki te b+10.

$$x=\frac{3\left(6b-5\right)}{b+10}$$

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{3}{2},5.

$$x=\frac{3\left(6b-5\right)}{b+10}\text{, }x\neq -\frac{3}{2}\text{ and }x\neq 5$$