Whakaoti i te 6/4x^2+12x+9+4x/2x+3=2

$$\frac { 6 } { 4 x ^ { 2 } + 12 x + 9 } + \frac { 4 x } { 2 x + 3 } = 2$$

Whakaoti mō x

$$x=-1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki -\frac{3}{2} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(2x+3\right)^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o 4x^{2}+12x+9,2x+3.

$$6+\left(2x+3\right)\times 4x=2\left(2x+3\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x+3 ki te 4.

$$6+\left(8x+12\right)x=2\left(2x+3\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8x+12 ki te x.

$$6+8x^{2}+12x=2\left(2x+3\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+3\right)^{2}.

$$6+8x^{2}+12x=2\left(4x^{2}+12x+9\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 4x^{2}+12x+9.

$$6+8x^{2}+12x=8x^{2}+24x+18$$

Tangohia te 8x^{2} mai i ngā taha e rua.

$$6+8x^{2}+12x-8x^{2}=24x+18$$

Pahekotia te 8x^{2} me -8x^{2}, ka 0.

$$6+12x=24x+18$$

Tangohia te 24x mai i ngā taha e rua.

$$6+12x-24x=18$$

Pahekotia te 12x me -24x, ka -12x.

$$6-12x=18$$

Tangohia te 6 mai i ngā taha e rua.

$$-12x=18-6$$

Tangohia te 6 i te 18, ka 12.

$$-12x=12$$

Whakawehea ngā taha e rua ki te -12.

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

Whakawehea te 12 ki te -12, kia riro ko -1.

$$x=-1$$