Whakaoti i te y-3/y-5=y-1/y-7

$$\frac { y - 3 } { y - 5 } = \frac { y - 1 } { y - 7 }$$

Whakaoti mō y

$$y=4$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe y ki tētahi o ngā uara 5,7 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(y-7\right)\left(y-5\right), arā, te tauraro pātahi he tino iti rawa te kitea o y-5,y-7.

$$\left(y-7\right)\left(y-3\right)=\left(y-5\right)\left(y-1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te y-7 ki te y-3 ka whakakotahi i ngā kupu rite.

$$y^{2}-10y+21=\left(y-5\right)\left(y-1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te y-5 ki te y-1 ka whakakotahi i ngā kupu rite.

$$y^{2}-10y+21=y^{2}-6y+5$$

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

$$y^{2}-10y+21-y^{2}=-6y+5$$

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

$$-10y+21=-6y+5$$

Me tāpiri te 6y ki ngā taha e rua.

$$-10y+21+6y=5$$

Pahekotia te -10y me 6y, ka -4y.

$$-4y+21=5$$

Tangohia te 21 mai i ngā taha e rua.

$$-4y=5-21$$

Tangohia te 21 i te 5, ka -16.

$$-4y=-16$$

Whakawehea ngā taha e rua ki te -4.

$$y=\frac{-16}{-4}$$

Whakawehea te -16 ki te -4, kia riro ko 4.

$$y=4$$