Whakaoti i te sqrt{4/3+1/9-1/12}:x=(1/3+frac{1}{2}):sqrt{(frac{1}{9}+frac{4}{3}*frac{3}{5}-frac{4}{15}):frac{29}{5}}

$$\sqrt { \frac { 4 } { 3 } + \frac { 1 } { 9 } - \frac { 1 } { 12 } } : x = ( \frac { 1 } { 3 } + \frac { 1 } { 2 } ) : \sqrt { ( \frac { 1 } { 9 } + \frac { 4 } { 3 } \cdot \frac { 3 } { 5 } - \frac { 4 } { 15 } ) : \frac { 29 } { 5 } }$$

Whakaoti mō x

$$x=\frac{7}{15}\approx 0.466666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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.

$$\sqrt{\frac{4}{3}+\frac{1}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Ko te maha noa iti rawa atu o 3 me 9 ko 9. Me tahuri \frac{4}{3} me \frac{1}{9} ki te hautau me te tautūnga 9.

$$\sqrt{\frac{12}{9}+\frac{1}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Tā te mea he rite te tauraro o \frac{12}{9} me \frac{1}{9}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{12+1}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Tāpirihia te 12 ki te 1, ka 13.

$$\sqrt{\frac{13}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Ko te maha noa iti rawa atu o 9 me 12 ko 36. Me tahuri \frac{13}{9} me \frac{1}{12} ki te hautau me te tautūnga 36.

$$\sqrt{\frac{52}{36}-\frac{3}{36}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Tā te mea he rite te tauraro o \frac{52}{36} me \frac{3}{36}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{52-3}{36}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Tangohia te 3 i te 52, ka 49.

$$\sqrt{\frac{49}{36}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Tuhia anō te pūtake rua o te whakawehenga \frac{49}{36} hei whakawehenga o ngā pūtake rua \frac{\sqrt{49}}{\sqrt{36}}. Tuhia te pūtakerua o te taurunga me te tauraro.

$$\frac{7}{6}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Ko te maha noa iti rawa atu o 3 me 2 ko 6. Me tahuri \frac{1}{3} me \frac{1}{2} ki te hautau me te tautūnga 6.

$$\frac{7}{6}=3x\left(\frac{2}{6}+\frac{3}{6}\right)$$

Tā te mea he rite te tauraro o \frac{2}{6} me \frac{3}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{7}{6}=3x\times \frac{2+3}{6}$$

Tāpirihia te 2 ki te 3, ka 5.

$$\frac{7}{6}=3x\times \frac{5}{6}$$

Tuhia te 3\times \frac{5}{6} hei hautanga kotahi.

$$\frac{7}{6}=\frac{3\times 5}{6}x$$

Whakareatia te 3 ki te 5, ka 15.

$$\frac{7}{6}=\frac{15}{6}x$$

Whakahekea te hautanga \frac{15}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{7}{6}=\frac{5}{2}x$$

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

$$\frac{5}{2}x=\frac{7}{6}$$

Me whakarea ngā taha e rua ki te \frac{2}{5}, te tau utu o \frac{5}{2}.

$$x=\frac{7}{6}\times \frac{2}{5}$$

Me whakarea te \frac{7}{6} ki te \frac{2}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{7\times 2}{6\times 5}$$

Mahia ngā whakarea i roto i te hautanga \frac{7\times 2}{6\times 5}.

$$x=\frac{14}{30}$$

Whakahekea te hautanga \frac{14}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{7}{15}$$