Whakaoti i te by-5/y+2=-4/3

$$\frac { b y - 5 } { y + 2 } = \frac { - 4 } { 3 }$$

Whakaoti mō b

$$b=-\frac{4}{3}+\frac{7}{3y}$$

$$y\neq 0\text{ and }y\neq -2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$3\left(by-5\right)=\left(y+2\right)\left(-4\right)$$

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

$$3by-15=\left(y+2\right)\left(-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te y+2 ki te -4.

$$3by-15=-4y-8$$

Me tāpiri te 15 ki ngā taha e rua.

$$3by=-4y-8+15$$

Tāpirihia te -8 ki te 15, ka 7.

$$3by=-4y+7$$

He hanga arowhānui tō te whārite.

$$3yb=7-4y$$

Whakawehea ngā taha e rua ki te 3y.

$$\frac{3yb}{3y}=\frac{7-4y}{3y}$$

Mā te whakawehe ki te 3y ka wetekia te whakareanga ki te 3y.

$$b=\frac{7-4y}{3y}$$

Whakawehe -4y+7 ki te 3y.

$$b=-\frac{4}{3}+\frac{7}{3y}$$

Whakaoti mō y

$$y=\frac{7}{3b+4}$$

$$b\neq -\frac{5}{2}\text{ and }b\neq -\frac{4}{3}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$3\left(by-5\right)=\left(y+2\right)\left(-4\right)$$

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

$$3by-15=\left(y+2\right)\left(-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te y+2 ki te -4.

$$3by-15=-4y-8$$

Me tāpiri te 4y ki ngā taha e rua.

$$3by-15+4y=-8$$

Me tāpiri te 15 ki ngā taha e rua.

$$3by+4y=-8+15$$

Tāpirihia te -8 ki te 15, ka 7.

$$3by+4y=7$$

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

$$\left(3b+4\right)y=7$$

Whakawehea ngā taha e rua ki te 4+3b.

$$\frac{\left(3b+4\right)y}{3b+4}=\frac{7}{3b+4}$$

Mā te whakawehe ki te 4+3b ka wetekia te whakareanga ki te 4+3b.

$$y=\frac{7}{3b+4}$$

Tē taea kia ōrite te tāupe y ki -2.

$$y=\frac{7}{3b+4}\text{, }y\neq -2$$