Whakaoti i te 1/x+3-2/5x-20=3/2(3x-12)-2/x+3

$$\frac { 1 } { x + 3 } - \frac { 2 } { 5 x - 20 } = \frac { 3 } { 2 ( 3 x - 12 ) } - \frac { 2 } { x + 3 }$$

Whakaoti mō x

$$x=7$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -3,4 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 30\left(x-4\right)\left(x+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+3,5x-20,2\left(3x-12\right).

$$30x-120-\left(6x+18\right)\times 2=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x+18 ki te 2.

$$30x-120-\left(12x+36\right)=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

Hei kimi i te tauaro o 12x+36, kimihia te tauaro o ia taurangi.

$$30x-120-12x-36=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

Pahekotia te 30x me -12x, ka 18x.

$$18x-120-36=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

Tangohia te 36 i te -120, ka -156.

$$18x-156=\left(5x+15\right)\times 3-\left(30x-120\right)\times 2$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5x+15 ki te 3.

$$18x-156=15x+45-\left(30x-120\right)\times 2$$

Whakamahia te āhuatanga tohatoha hei whakarea te 30x-120 ki te 2.

$$18x-156=15x+45-\left(60x-240\right)$$

Hei kimi i te tauaro o 60x-240, kimihia te tauaro o ia taurangi.

$$18x-156=15x+45-60x+240$$

Pahekotia te 15x me -60x, ka -45x.

$$18x-156=-45x+45+240$$

Tāpirihia te 45 ki te 240, ka 285.

$$18x-156=-45x+285$$

Me tāpiri te 45x ki ngā taha e rua.

$$18x-156+45x=285$$

Pahekotia te 18x me 45x, ka 63x.

$$63x-156=285$$

Me tāpiri te 156 ki ngā taha e rua.

$$63x=285+156$$

Tāpirihia te 285 ki te 156, ka 441.

$$63x=441$$

Whakawehea ngā taha e rua ki te 63.

$$x=\frac{441}{63}$$

Whakawehea te 441 ki te 63, kia riro ko 7.

$$x=7$$