Whakaoti i te 3/2x+1=2/2x-1-x+1/4x^2-1

$$\frac { 3 } { 2 x + 1 } = \frac { 2 } { 2 x - 1 } - \frac { x + 1 } { 4 x ^ { 2 } - 1 }$$

Whakaoti mō x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{1}{2},\frac{1}{2} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(2x-1\right)\left(2x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x+1,2x-1,4x^{2}-1.

$$\left(2x-1\right)\times 3=\left(2x+1\right)\times 2-\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x-1 ki te 3.

$$6x-3=\left(2x+1\right)\times 2-\left(x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x+1 ki te 2.

$$6x-3=4x+2-\left(x+1\right)$$

Hei kimi i te tauaro o x+1, kimihia te tauaro o ia taurangi.

$$6x-3=4x+2-x-1$$

Pahekotia te 4x me -x, ka 3x.

$$6x-3=3x+2-1$$

Tangohia te 1 i te 2, ka 1.

$$6x-3=3x+1$$

Tangohia te 3x mai i ngā taha e rua.

$$6x-3-3x=1$$

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

$$3x-3=1$$

Me tāpiri te 3 ki ngā taha e rua.

$$3x=1+3$$

Tāpirihia te 1 ki te 3, ka 4.

$$3x=4$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{4}{3}$$