Whakaoti i te 5/y-2-2y-2/y^2-4=6/y+2

$$\frac { 5 } { y - 2 } - \frac { 2 y - 2 } { y ^ { 2 } - 4 } = \frac { 6 } { y + 2 }$$

Whakaoti mō y

$$y=8$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe y ki tētahi o ngā uara -2,2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(y-2\right)\left(y+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o y-2,y^{2}-4,y+2.

$$\left(y+2\right)\times 5-\left(2y-2\right)=\left(y-2\right)\times 6$$

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

$$5y+10-\left(2y-2\right)=\left(y-2\right)\times 6$$

Hei kimi i te tauaro o 2y-2, kimihia te tauaro o ia taurangi.

$$5y+10-2y+2=\left(y-2\right)\times 6$$

Pahekotia te 5y me -2y, ka 3y.

$$3y+10+2=\left(y-2\right)\times 6$$

Tāpirihia te 10 ki te 2, ka 12.

$$3y+12=\left(y-2\right)\times 6$$

Whakamahia te āhuatanga tohatoha hei whakarea te y-2 ki te 6.

$$3y+12=6y-12$$

Tangohia te 6y mai i ngā taha e rua.

$$3y+12-6y=-12$$

Pahekotia te 3y me -6y, ka -3y.

$$-3y+12=-12$$

Tangohia te 12 mai i ngā taha e rua.

$$-3y=-12-12$$

Tangohia te 12 i te -12, ka -24.

$$-3y=-24$$

Whakawehea ngā taha e rua ki te -3.

$$y=\frac{-24}{-3}$$

Whakawehea te -24 ki te -3, kia riro ko 8.

$$y=8$$