Whakaoti i te 1-3/x/1+frac{3{x}}=2/3

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

Whakaoti mō x

$$x=15$$

Ngā Upane Whakamahi Tauwehe

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{x}{x}.

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

Tā te mea he rite te tauraro o \frac{x}{x} me \frac{3}{x}, me tango rāua mā te tango i ō raua taurunga.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{x}{x}.

$$\frac{\frac{x-3}{x}}{\frac{x}{x}+\frac{3}{x}}=\frac{2}{3}$$

Tā te mea he rite te tauraro o \frac{x}{x} me \frac{3}{x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{x-3}{x}}{\frac{x+3}{x}}=\frac{2}{3}$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakawehe \frac{x-3}{x} ki te \frac{x+3}{x} mā te whakarea \frac{x-3}{x} ki te tau huripoki o \frac{x+3}{x}.

$$\frac{\left(x-3\right)x}{x\left(x+3\right)}=\frac{2}{3}$$

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

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

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

$$\frac{x^{2}-3x}{x^{2}+3x}=\frac{2}{3}$$

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -3,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3x\left(x+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}+3x,3.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}-3x.

$$3x^{2}-9x=2x\left(x+3\right)$$

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

$$3x^{2}-9x=2x^{2}+6x$$

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

$$3x^{2}-9x-2x^{2}=6x$$

Pahekotia te 3x^{2} me -2x^{2}, ka x^{2}.

$$x^{2}-9x=6x$$

Tangohia te 6x mai i ngā taha e rua.

$$x^{2}-9x-6x=0$$

Pahekotia te -9x me -6x, ka -15x.

$$x^{2}-15x=0$$

Tauwehea te x.

$$x\left(x-15\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te x-15=0.

$$x=0 x=15$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=15$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{x}{x}.

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

Tā te mea he rite te tauraro o \frac{x}{x} me \frac{3}{x}, me tango rāua mā te tango i ō raua taurunga.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{x}{x}.

$$\frac{\frac{x-3}{x}}{\frac{x}{x}+\frac{3}{x}}=\frac{2}{3}$$

Tā te mea he rite te tauraro o \frac{x}{x} me \frac{3}{x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{x-3}{x}}{\frac{x+3}{x}}=\frac{2}{3}$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakawehe \frac{x-3}{x} ki te \frac{x+3}{x} mā te whakarea \frac{x-3}{x} ki te tau huripoki o \frac{x+3}{x}.

$$\frac{\left(x-3\right)x}{x\left(x+3\right)}=\frac{2}{3}$$

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

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

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

$$\frac{x^{2}-3x}{x^{2}+3x}=\frac{2}{3}$$

Tangohia te \frac{2}{3} mai i ngā taha e rua.

$$\frac{x^{2}-3x}{x^{2}+3x}-\frac{2}{3}=0$$

Tauwehea te x^{2}+3x.

$$\frac{x^{2}-3x}{x\left(x+3\right)}-\frac{2}{3}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o x\left(x+3\right) me 3 ko 3x\left(x+3\right). Whakareatia \frac{x^{2}-3x}{x\left(x+3\right)} ki te \frac{3}{3}. Whakareatia \frac{2}{3} ki te \frac{x\left(x+3\right)}{x\left(x+3\right)}.

$$\frac{3\left(x^{2}-3x\right)}{3x\left(x+3\right)}-\frac{2x\left(x+3\right)}{3x\left(x+3\right)}=0$$

Tā te mea he rite te tauraro o \frac{3\left(x^{2}-3x\right)}{3x\left(x+3\right)} me \frac{2x\left(x+3\right)}{3x\left(x+3\right)}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3\left(x^{2}-3x\right)-2x\left(x+3\right)}{3x\left(x+3\right)}=0$$

Mahia ngā whakarea i roto o 3\left(x^{2}-3x\right)-2x\left(x+3\right).

$$\frac{3x^{2}-9x-2x^{2}-6x}{3x\left(x+3\right)}=0$$

Whakakotahitia ngā kupu rite i 3x^{2}-9x-2x^{2}-6x.

$$\frac{x^{2}-15x}{3x\left(x+3\right)}=0$$

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -3,0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 3x\left(x+3\right).

$$x^{2}-15x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -15 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}}}{2}$$

Tuhia te pūtakerua o te \left(-15\right)^{2}.

$$x=\frac{-\left(-15\right)±15}{2}$$

Ko te tauaro o -15 ko 15.

$$x=\frac{15±15}{2}$$

Nā, me whakaoti te whārite x=\frac{15±15}{2} ina he tāpiri te ±. Tāpiri 15 ki te 15.

$$x=\frac{30}{2}$$

Whakawehe 30 ki te 2.

$$x=15$$

Nā, me whakaoti te whārite x=\frac{15±15}{2} ina he tango te ±. Tango 15 mai i 15.

$$x=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=15 x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=15$$

Ngā Upane mō te Whakaoti i te Pūrua

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{x}{x}.

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

Tā te mea he rite te tauraro o \frac{x}{x} me \frac{3}{x}, me tango rāua mā te tango i ō raua taurunga.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{x}{x}.

$$\frac{\frac{x-3}{x}}{\frac{x}{x}+\frac{3}{x}}=\frac{2}{3}$$

Tā te mea he rite te tauraro o \frac{x}{x} me \frac{3}{x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{x-3}{x}}{\frac{x+3}{x}}=\frac{2}{3}$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakawehe \frac{x-3}{x} ki te \frac{x+3}{x} mā te whakarea \frac{x-3}{x} ki te tau huripoki o \frac{x+3}{x}.

$$\frac{\left(x-3\right)x}{x\left(x+3\right)}=\frac{2}{3}$$

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

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

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

$$\frac{x^{2}-3x}{x^{2}+3x}=\frac{2}{3}$$

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -3,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3x\left(x+3\right), arā, te tauraro pātahi he tino iti rawa te kitea o x^{2}+3x,3.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}-3x.

$$3x^{2}-9x=2x\left(x+3\right)$$

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

$$3x^{2}-9x=2x^{2}+6x$$

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

$$3x^{2}-9x-2x^{2}=6x$$

Pahekotia te 3x^{2} me -2x^{2}, ka x^{2}.

$$x^{2}-9x=6x$$

Tangohia te 6x mai i ngā taha e rua.

$$x^{2}-9x-6x=0$$

Pahekotia te -9x me -6x, ka -15x.

$$x^{2}-15x=0$$

Whakawehea te -15, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{15}{2}. Nā, tāpiria te pūrua o te -\frac{15}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-15x+\left(-\frac{15}{2}\right)^{2}=\left(-\frac{15}{2}\right)^{2}$$

Pūruatia -\frac{15}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-15x+\frac{225}{4}=\frac{225}{4}$$

Tauwehea x^{2}-15x+\frac{225}{4}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{15}{2}\right)^{2}=\frac{225}{4}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x-\frac{15}{2}\right)^{2}}=\sqrt{\frac{225}{4}}$$

Whakarūnātia.

$$x-\frac{15}{2}=\frac{15}{2} x-\frac{15}{2}=-\frac{15}{2}$$

Me tāpiri \frac{15}{2} ki ngā taha e rua o te whārite.

$$x=15 x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=15$$