Whakaoti i te 4/9y^2-1-4/3y+1=5/1-3y

$$\frac { 4 } { 9 y ^ { 2 } - 1 } - \frac { 4 } { 3 y + 1 } = \frac { 5 } { 1 - 3 y }$$

Whakaoti mō y

$$y = -\frac{13}{3} = -4\frac{1}{3} \approx -4.333333333$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe y ki tētahi o ngā uara -\frac{1}{3},\frac{1}{3} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(3y-1\right)\left(3y+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 9y^{2}-1,3y+1,1-3y.

$$4-\left(3y-1\right)\times 4=\left(-1-3y\right)\times 5$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3y-1 ki te 4.

$$4-\left(12y-4\right)=\left(-1-3y\right)\times 5$$

Hei kimi i te tauaro o 12y-4, kimihia te tauaro o ia taurangi.

$$4-12y+4=\left(-1-3y\right)\times 5$$

Tāpirihia te 4 ki te 4, ka 8.

$$8-12y=\left(-1-3y\right)\times 5$$

Whakamahia te āhuatanga tohatoha hei whakarea te -1-3y ki te 5.

$$8-12y=-5-15y$$

Me tāpiri te 15y ki ngā taha e rua.

$$8-12y+15y=-5$$

Pahekotia te -12y me 15y, ka 3y.

$$8+3y=-5$$

Tangohia te 8 mai i ngā taha e rua.

$$3y=-5-8$$

Tangohia te 8 i te -5, ka -13.

$$3y=-13$$

Whakawehea ngā taha e rua ki te 3.

$$y=\frac{-13}{3}$$

Ka taea te hautanga \frac{-13}{3} te tuhi anō ko -\frac{13}{3} mā te tango i te tohu tōraro.

$$y=-\frac{13}{3}$$