Whakaoti i te 5/6x+5+x/5=20/24x+20

$$\frac { 5 } { 6 x + 5 } + \frac { x } { 5 } = \frac { 20 } { 24 x + 20 }$$

Whakaoti mō x

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki -\frac{5}{6} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 20\left(6x+5\right), arā, te tauraro pātahi he tino iti rawa te kitea o 6x+5,5,24x+20.

$$20\times 5+\left(24x+20\right)x=5\times 20$$

Whakareatia te 20 ki te 5, ka 100.

$$100+\left(24x+20\right)x=5\times 20$$

Whakamahia te āhuatanga tohatoha hei whakarea te 24x+20 ki te x.

$$100+24x^{2}+20x=5\times 20$$

Whakareatia te 5 ki te 20, ka 100.

$$100+24x^{2}+20x=100$$

Tangohia te 100 mai i ngā taha e rua.

$$100+24x^{2}+20x-100=0$$

Tangohia te 100 i te 100, ka 0.

$$24x^{2}+20x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 24 mō a, 20 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20±\sqrt{20^{2}}}{2\times 24}$$

Tuhia te pūtakerua o te 20^{2}.

$$x=\frac{-20±20}{2\times 24}$$

Whakareatia 2 ki te 24.

$$x=\frac{-20±20}{48}$$

Nā, me whakaoti te whārite x=\frac{-20±20}{48} ina he tāpiri te ±. Tāpiri -20 ki te 20.

$$x=\frac{0}{48}$$

Whakawehe 0 ki te 48.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-20±20}{48} ina he tango te ±. Tango 20 mai i -20.

$$x=-\frac{40}{48}$$

Whakahekea te hautanga \frac{-40}{48} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$x=-\frac{5}{6}$$

Kua oti te whārite te whakatau.

$$x=0 x=-\frac{5}{6}$$

Tē taea kia ōrite te tāupe x ki -\frac{5}{6}.

$$x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki -\frac{5}{6} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 20\left(6x+5\right), arā, te tauraro pātahi he tino iti rawa te kitea o 6x+5,5,24x+20.

$$20\times 5+\left(24x+20\right)x=5\times 20$$

Whakareatia te 20 ki te 5, ka 100.

$$100+\left(24x+20\right)x=5\times 20$$

Whakamahia te āhuatanga tohatoha hei whakarea te 24x+20 ki te x.

$$100+24x^{2}+20x=5\times 20$$

Whakareatia te 5 ki te 20, ka 100.

$$100+24x^{2}+20x=100$$

Tangohia te 100 mai i ngā taha e rua.

$$24x^{2}+20x=100-100$$

Tangohia te 100 i te 100, ka 0.

$$24x^{2}+20x=0$$

Whakawehea ngā taha e rua ki te 24.

$$\frac{24x^{2}+20x}{24}=\frac{0}{24}$$

Mā te whakawehe ki te 24 ka wetekia te whakareanga ki te 24.

$$x^{2}+\frac{20}{24}x=\frac{0}{24}$$

Whakahekea te hautanga \frac{20}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}+\frac{5}{6}x=\frac{0}{24}$$

Whakawehe 0 ki te 24.

$$x^{2}+\frac{5}{6}x=0$$

Whakawehea te \frac{5}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{12}. Nā, tāpiria te pūrua o te \frac{5}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{5}{6}x+\left(\frac{5}{12}\right)^{2}=\left(\frac{5}{12}\right)^{2}$$

Pūruatia \frac{5}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{5}{6}x+\frac{25}{144}=\frac{25}{144}$$

Tauwehea x^{2}+\frac{5}{6}x+\frac{25}{144}. 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}.

$$\left(x+\frac{5}{12}\right)^{2}=\frac{25}{144}$$

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

$$\sqrt{\left(x+\frac{5}{12}\right)^{2}}=\sqrt{\frac{25}{144}}$$

Whakarūnātia.

$$x+\frac{5}{12}=\frac{5}{12} x+\frac{5}{12}=-\frac{5}{12}$$

Me tango \frac{5}{12} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{5}{6}$$

Tē taea kia ōrite te tāupe x ki -\frac{5}{6}.

$$x=0$$