Whakaoti i te (8/5+1/3):x=x:(1+14/15)

$$( \frac { 8 } { 5 } + \frac { 1 } { 3 } ) : x = x : ( 1 + \frac { 14 } { 15 } )$$

Whakaoti mō x

$$x = \frac{29}{15} = 1\frac{14}{15} \approx 1.933333333$$

$$x = -\frac{29}{15} = -1\frac{14}{15} \approx -1.933333333$$

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.

$$\frac{8}{5}+\frac{1}{3}=\frac{15}{29}xx$$

Ko te maha noa iti rawa atu o 5 me 3 ko 15. Me tahuri \frac{8}{5} me \frac{1}{3} ki te hautau me te tautūnga 15.

$$\frac{24}{15}+\frac{5}{15}=\frac{15}{29}xx$$

Tā te mea he rite te tauraro o \frac{24}{15} me \frac{5}{15}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{24+5}{15}=\frac{15}{29}xx$$

Tāpirihia te 24 ki te 5, ka 29.

$$\frac{29}{15}=\frac{15}{29}xx$$

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

$$\frac{29}{15}=\frac{15}{29}x^{2}$$

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

$$\frac{15}{29}x^{2}=\frac{29}{15}$$

Me whakarea ngā taha e rua ki te \frac{29}{15}, te tau utu o \frac{15}{29}.

$$x^{2}=\frac{29}{15}\times \frac{29}{15}$$

Me whakarea te \frac{29}{15} ki te \frac{29}{15} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x^{2}=\frac{29\times 29}{15\times 15}$$

Mahia ngā whakarea i roto i te hautanga \frac{29\times 29}{15\times 15}.

$$x^{2}=\frac{841}{225}$$

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

$$x=\frac{29}{15} x=-\frac{29}{15}$$

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.

$$\frac{8}{5}+\frac{1}{3}=\frac{15}{29}xx$$

Ko te maha noa iti rawa atu o 5 me 3 ko 15. Me tahuri \frac{8}{5} me \frac{1}{3} ki te hautau me te tautūnga 15.

$$\frac{24}{15}+\frac{5}{15}=\frac{15}{29}xx$$

Tā te mea he rite te tauraro o \frac{24}{15} me \frac{5}{15}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{24+5}{15}=\frac{15}{29}xx$$

Tāpirihia te 24 ki te 5, ka 29.

$$\frac{29}{15}=\frac{15}{29}xx$$

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

$$\frac{29}{15}=\frac{15}{29}x^{2}$$

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

$$\frac{15}{29}x^{2}=\frac{29}{15}$$

Tangohia te \frac{29}{15} mai i ngā taha e rua.

$$\frac{15}{29}x^{2}-\frac{29}{15}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{15}{29} mō a, 0 mō b, me -\frac{29}{15} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{15}{29}\left(-\frac{29}{15}\right)}}{2\times \frac{15}{29}}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times \frac{15}{29}\left(-\frac{29}{15}\right)}}{2\times \frac{15}{29}}$$

Whakareatia -4 ki te \frac{15}{29}.

$$x=\frac{0±\sqrt{-\frac{60}{29}\left(-\frac{29}{15}\right)}}{2\times \frac{15}{29}}$$

Whakareatia -\frac{60}{29} ki te -\frac{29}{15} 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.

$$x=\frac{0±\sqrt{4}}{2\times \frac{15}{29}}$$

Tuhia te pūtakerua o te 4.

$$x=\frac{0±2}{2\times \frac{15}{29}}$$

Whakareatia 2 ki te \frac{15}{29}.

$$x=\frac{0±2}{\frac{30}{29}}$$

Nā, me whakaoti te whārite x=\frac{0±2}{\frac{30}{29}} ina he tāpiri te ±. Whakawehe 2 ki te \frac{30}{29} mā te whakarea 2 ki te tau huripoki o \frac{30}{29}.

$$x=\frac{29}{15}$$

Nā, me whakaoti te whārite x=\frac{0±2}{\frac{30}{29}} ina he tango te ±. Whakawehe -2 ki te \frac{30}{29} mā te whakarea -2 ki te tau huripoki o \frac{30}{29}.

$$x=-\frac{29}{15}$$

Kua oti te whārite te whakatau.

$$x=\frac{29}{15} x=-\frac{29}{15}$$