Whakaoti i te x-24/2x^2-9x-18=x/x-6-2x/2x+3

$$\frac { x - 24 } { 2 x ^ { 2 } - 9 x - 18 } = \frac { x } { x - 6 } - \frac { 2 x } { 2 x + 3 }$$

Whakaoti mō x

$$x = -\frac{12}{7} = -1\frac{5}{7} \approx -1.714285714$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -\frac{3}{2},6 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-6\right)\left(2x+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 2x^{2}-9x-18,x-6,2x+3.

$$x-24=\left(2x+3\right)x-\left(x-6\right)\times 2x$$

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

$$x-24=2x^{2}+3x-\left(x-6\right)\times 2x$$

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

$$x-24=2x^{2}+3x-\left(2x-12\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x-12 ki te x.

$$x-24=2x^{2}+3x-\left(2x^{2}-12x\right)$$

Hei kimi i te tauaro o 2x^{2}-12x, kimihia te tauaro o ia taurangi.

$$x-24=2x^{2}+3x-2x^{2}+12x$$

Pahekotia te 2x^{2} me -2x^{2}, ka 0.

$$x-24=3x+12x$$

Pahekotia te 3x me 12x, ka 15x.

$$x-24=15x$$

Tangohia te 15x mai i ngā taha e rua.

$$x-24-15x=0$$

Pahekotia te x me -15x, ka -14x.

$$-14x-24=0$$

Me tāpiri te 24 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$-14x=24$$

Whakawehea ngā taha e rua ki te -14.

$$x=\frac{24}{-14}$$

Whakahekea te hautanga \frac{24}{-14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{12}{7}$$