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

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

Whakaoti mō x

$$x = \frac{17}{8} = 2\frac{1}{8} = 2.125$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x+3.

$$2x+6-\left(2x+5\right)=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

Hei kimi i te tauaro o 2x+5, kimihia te tauaro o ia taurangi.

$$2x+6-2x-5=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

Pahekotia te 2x me -2x, ka 0.

$$6-5=2\left(x-2\right)\times 3+\left(x-2\right)\times 2$$

Tangohia te 5 i te 6, ka 1.

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

Whakareatia te 2 ki te 3, ka 6.

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

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

$$1=6x-12+\left(x-2\right)\times 2$$

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

$$1=6x-12+2x-4$$

Pahekotia te 6x me 2x, ka 8x.

$$1=8x-12-4$$

Tangohia te 4 i te -12, ka -16.

$$1=8x-16$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$8x-16=1$$

Me tāpiri te 16 ki ngā taha e rua.

$$8x=1+16$$

Tāpirihia te 1 ki te 16, ka 17.

$$8x=17$$

Whakawehea ngā taha e rua ki te 8.

$$x=\frac{17}{8}$$