Whakaoti i te 11/8left(3/11+1/6+frac{3/2right)}{x}=frac{x}{frac{frac{5}{3}-frac{1}{4}+frac{3}{2}}{frac{7}{6}}frac{20}{3}}

$$\frac{ \frac{ 11 }{ 8 } \left( \frac{ 3 }{ 11 } + \frac{ 1 }{ 6 } + \frac{ 3 }{ 2 } \right) }{ x } = \frac{ x }{ \frac{ \frac{ 5 }{ 3 } - \frac{ 1 }{ 4 } + \frac{ 3 }{ 2 } }{ \frac{ 7 }{ 6 } } \frac{ 20 }{ 3 } }$$

Whakaoti mō x

$$x = \frac{20}{3} = 6\frac{2}{3} \approx 6.666666667$$

$$x = -\frac{20}{3} = -6\frac{2}{3} \approx -6.666666667$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$\frac{11}{8}\left(\frac{3}{11}+\frac{1}{6}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Ko te maha noa iti rawa atu o 11 me 6 ko 66. Me tahuri \frac{3}{11} me \frac{1}{6} ki te hautau me te tautūnga 66.

$$\frac{11}{8}\left(\frac{18}{66}+\frac{11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Tā te mea he rite te tauraro o \frac{18}{66} me \frac{11}{66}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{11}{8}\left(\frac{18+11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Tāpirihia te 18 ki te 11, ka 29.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Ko te maha noa iti rawa atu o 66 me 2 ko 66. Me tahuri \frac{29}{66} me \frac{3}{2} ki te hautau me te tautūnga 66.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{99}{66}\right)=\frac{3}{50}xx$$

Tā te mea he rite te tauraro o \frac{29}{66} me \frac{99}{66}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{11}{8}\times \frac{29+99}{66}=\frac{3}{50}xx$$

Tāpirihia te 29 ki te 99, ka 128.

$$\frac{11}{8}\times \frac{128}{66}=\frac{3}{50}xx$$

Whakahekea te hautanga \frac{128}{66} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{11}{8}\times \frac{64}{33}=\frac{3}{50}xx$$

Me whakarea te \frac{11}{8} ki te \frac{64}{33} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{11\times 64}{8\times 33}=\frac{3}{50}xx$$

Mahia ngā whakarea i roto i te hautanga \frac{11\times 64}{8\times 33}.

$$\frac{704}{264}=\frac{3}{50}xx$$

Whakahekea te hautanga \frac{704}{264} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 88.

$$\frac{8}{3}=\frac{3}{50}xx$$

Whakareatia te x ki te x, ka x^{2}.

$$\frac{8}{3}=\frac{3}{50}x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{3}{50}x^{2}=\frac{8}{3}$$

Me whakarea ngā taha e rua ki te \frac{50}{3}, te tau utu o \frac{3}{50}.

$$x^{2}=\frac{8}{3}\times \frac{50}{3}$$

Me whakarea te \frac{8}{3} ki te \frac{50}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x^{2}=\frac{8\times 50}{3\times 3}$$

Mahia ngā whakarea i roto i te hautanga \frac{8\times 50}{3\times 3}.

$$x^{2}=\frac{400}{9}$$

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

$$x=\frac{20}{3} x=-\frac{20}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$\frac{11}{8}\left(\frac{3}{11}+\frac{1}{6}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Ko te maha noa iti rawa atu o 11 me 6 ko 66. Me tahuri \frac{3}{11} me \frac{1}{6} ki te hautau me te tautūnga 66.

$$\frac{11}{8}\left(\frac{18}{66}+\frac{11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Tā te mea he rite te tauraro o \frac{18}{66} me \frac{11}{66}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{11}{8}\left(\frac{18+11}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Tāpirihia te 18 ki te 11, ka 29.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{3}{2}\right)=\frac{3}{50}xx$$

Ko te maha noa iti rawa atu o 66 me 2 ko 66. Me tahuri \frac{29}{66} me \frac{3}{2} ki te hautau me te tautūnga 66.

$$\frac{11}{8}\left(\frac{29}{66}+\frac{99}{66}\right)=\frac{3}{50}xx$$

Tā te mea he rite te tauraro o \frac{29}{66} me \frac{99}{66}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{11}{8}\times \frac{29+99}{66}=\frac{3}{50}xx$$

Tāpirihia te 29 ki te 99, ka 128.

$$\frac{11}{8}\times \frac{128}{66}=\frac{3}{50}xx$$

Whakahekea te hautanga \frac{128}{66} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{11}{8}\times \frac{64}{33}=\frac{3}{50}xx$$

Me whakarea te \frac{11}{8} ki te \frac{64}{33} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{11\times 64}{8\times 33}=\frac{3}{50}xx$$

Mahia ngā whakarea i roto i te hautanga \frac{11\times 64}{8\times 33}.

$$\frac{704}{264}=\frac{3}{50}xx$$

Whakahekea te hautanga \frac{704}{264} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 88.

$$\frac{8}{3}=\frac{3}{50}xx$$

Whakareatia te x ki te x, ka x^{2}.

$$\frac{8}{3}=\frac{3}{50}x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\frac{3}{50}x^{2}=\frac{8}{3}$$

Tangohia te \frac{8}{3} mai i ngā taha e rua.

$$\frac{3}{50}x^{2}-\frac{8}{3}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{3}{50} mō a, 0 mō b, me -\frac{8}{3} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{50}\left(-\frac{8}{3}\right)}}{2\times \frac{3}{50}}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{50}\left(-\frac{8}{3}\right)}}{2\times \frac{3}{50}}$$

Whakareatia -4 ki te \frac{3}{50}.

$$x=\frac{0±\sqrt{-\frac{6}{25}\left(-\frac{8}{3}\right)}}{2\times \frac{3}{50}}$$

Whakareatia -\frac{6}{25} ki te -\frac{8}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{0±\sqrt{\frac{16}{25}}}{2\times \frac{3}{50}}$$

Tuhia te pūtakerua o te \frac{16}{25}.

$$x=\frac{0±\frac{4}{5}}{2\times \frac{3}{50}}$$

Whakareatia 2 ki te \frac{3}{50}.

$$x=\frac{0±\frac{4}{5}}{\frac{3}{25}}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{4}{5}}{\frac{3}{25}} ina he tāpiri te ±.

$$x=\frac{20}{3}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{4}{5}}{\frac{3}{25}} ina he tango te ±.

$$x=-\frac{20}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{20}{3} x=-\frac{20}{3}$$