Whakaoti i te 1/6-2x-4/5-5x=10/12-4x-3/10-10x

$$\frac { 1 } { 6 - 2 x } - \frac { 4 } { 5 - 5 x } = \frac { 10 } { 12 - 4 x } - \frac { 3 } { 10 - 10 x }$$

Whakaoti mō x

$$x = \frac{7}{5} = 1\frac{2}{5} = 1.4$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 1,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 20\left(x-3\right)\left(x-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o 6-2x,5-5x,12-4x,10-10x.

$$10-10x-\left(12-4x\right)\times 4=\left(5-5x\right)\times 10-\left(6-2x\right)\times 3$$

Whakamahia te āhuatanga tohatoha hei whakarea te 12-4x ki te 4.

$$10-10x-\left(48-16x\right)=\left(5-5x\right)\times 10-\left(6-2x\right)\times 3$$

Hei kimi i te tauaro o 48-16x, kimihia te tauaro o ia taurangi.

$$10-10x-48+16x=\left(5-5x\right)\times 10-\left(6-2x\right)\times 3$$

Tangohia te 48 i te 10, ka -38.

$$-38-10x+16x=\left(5-5x\right)\times 10-\left(6-2x\right)\times 3$$

Pahekotia te -10x me 16x, ka 6x.

$$-38+6x=\left(5-5x\right)\times 10-\left(6-2x\right)\times 3$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5-5x ki te 10.

$$-38+6x=50-50x-\left(6-2x\right)\times 3$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6-2x ki te 3.

$$-38+6x=50-50x-\left(18-6x\right)$$

Hei kimi i te tauaro o 18-6x, kimihia te tauaro o ia taurangi.

$$-38+6x=50-50x-18+6x$$

Tangohia te 18 i te 50, ka 32.

$$-38+6x=32-50x+6x$$

Pahekotia te -50x me 6x, ka -44x.

$$-38+6x=32-44x$$

Me tāpiri te 44x ki ngā taha e rua.

$$-38+6x+44x=32$$

Pahekotia te 6x me 44x, ka 50x.

$$-38+50x=32$$

Me tāpiri te 38 ki ngā taha e rua.

$$50x=32+38$$

Tāpirihia te 32 ki te 38, ka 70.

$$50x=70$$

Whakawehea ngā taha e rua ki te 50.

$$x=\frac{70}{50}$$

Whakahekea te hautanga \frac{70}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$x=\frac{7}{5}$$