Whakaoti i te 3/2x-2+5/x+1=4/x-1

$$\frac { 3 } { 2 x - 2 } + \frac { 5 } { x + 1 } = \frac { 4 } { x - 1 }$$

Whakaoti mō x

$$x=3$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$\left(x+1\right)\times 3+\left(2x-2\right)\times 5=\left(2x+2\right)\times 4$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+1 ki te 3.

$$3x+3+\left(2x-2\right)\times 5=\left(2x+2\right)\times 4$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x-2 ki te 5.

$$3x+3+10x-10=\left(2x+2\right)\times 4$$

Pahekotia te 3x me 10x, ka 13x.

$$13x+3-10=\left(2x+2\right)\times 4$$

Tangohia te 10 i te 3, ka -7.

$$13x-7=\left(2x+2\right)\times 4$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x+2 ki te 4.

$$13x-7=8x+8$$

Tangohia te 8x mai i ngā taha e rua.

$$13x-7-8x=8$$

Pahekotia te 13x me -8x, ka 5x.

$$5x-7=8$$

Me tāpiri te 7 ki ngā taha e rua.

$$5x=8+7$$

Tāpirihia te 8 ki te 7, ka 15.

$$5x=15$$

Whakawehea ngā taha e rua ki te 5.

$$x=\frac{15}{5}$$

Whakawehea te 15 ki te 5, kia riro ko 3.

$$x=3$$