Whakaoti i te 5x-4/x-1+2/3x-3-2x-7/2x-2=3

$$\frac { 5 x - 4 } { x - 1 } + \frac { 2 } { 3 x - 3 } - \frac { 2 x - 7 } { 2 x - 2 } = 3$$

Whakaoti mō x

$$x = -\frac{19}{6} = -3\frac{1}{6} \approx -3.166666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$6\left(5x-4\right)+2\times 2-3\left(2x-7\right)=18\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te 5x-4.

$$30x-24+2\times 2-3\left(2x-7\right)=18\left(x-1\right)$$

Whakareatia te 2 ki te 2, ka 4.

$$30x-24+4-3\left(2x-7\right)=18\left(x-1\right)$$

Tāpirihia te -24 ki te 4, ka -20.

$$30x-20-3\left(2x-7\right)=18\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3 ki te 2x-7.

$$30x-20-6x+21=18\left(x-1\right)$$

Pahekotia te 30x me -6x, ka 24x.

$$24x-20+21=18\left(x-1\right)$$

Tāpirihia te -20 ki te 21, ka 1.

$$24x+1=18\left(x-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 18 ki te x-1.

$$24x+1=18x-18$$

Tangohia te 18x mai i ngā taha e rua.

$$24x+1-18x=-18$$

Pahekotia te 24x me -18x, ka 6x.

$$6x+1=-18$$

Tangohia te 1 mai i ngā taha e rua.

$$6x=-18-1$$

Tangohia te 1 i te -18, ka -19.

$$6x=-19$$

Whakawehea ngā taha e rua ki te 6.

$$x=\frac{-19}{6}$$

Ka taea te hautanga \frac{-19}{6} te tuhi anō ko -\frac{19}{6} mā te tango i te tohu tōraro.

$$x=-\frac{19}{6}$$