Whakaoti i te x:(7/3*21/2-21)=sqrt{(5/3+4/3-frac{2}{6}):(frac{3}{6}+4-frac{1}{3})}:(frac{4}{5}+2)

$$x : ( \frac { 7 } { 3 } \cdot \frac { 21 } { 2 } - 21 ) = \sqrt { ( \frac { 5 } { 3 } + \frac { 4 } { 3 } - \frac { 2 } { 6 } ) : ( \frac { 3 } { 6 } + 4 - \frac { 1 } { 3 } ) } : ( \frac { 4 } { 5 } + 2 )$$

Whakaoti mō x

$$x=1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea te \frac{7}{3} ki te \frac{21}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{x}{\frac{7\times 21}{3\times 2}-21}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Mahia ngā whakarea i roto i te hautanga \frac{7\times 21}{3\times 2}.

$$\frac{x}{\frac{147}{6}-21}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Whakahekea te hautanga \frac{147}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{x}{\frac{49}{2}-21}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Me tahuri te 21 ki te hautau \frac{42}{2}.

$$\frac{x}{\frac{49}{2}-\frac{42}{2}}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Tā te mea he rite te tauraro o \frac{49}{2} me \frac{42}{2}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x}{\frac{49-42}{2}}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Tangohia te 42 i te 49, ka 7.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{5}{3}+\frac{4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Tā te mea he rite te tauraro o \frac{5}{3} me \frac{4}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{5+4}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Tāpirihia te 5 ki te 4, ka 9.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{9}{3}-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Whakawehea te 9 ki te 3, kia riro ko 3.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{3-\frac{2}{6}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Whakahekea te hautanga \frac{2}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{3-\frac{1}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Me tahuri te 3 ki te hautau \frac{9}{3}.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{9}{3}-\frac{1}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Tā te mea he rite te tauraro o \frac{9}{3} me \frac{1}{3}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{9-1}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Tangohia te 1 i te 9, ka 8.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{3}{6}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

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

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{1}{2}+4-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Me tahuri te 4 ki te hautau \frac{8}{2}.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{1}{2}+\frac{8}{2}-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Tā te mea he rite te tauraro o \frac{1}{2} me \frac{8}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{1+8}{2}-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Tāpirihia te 1 ki te 8, ka 9.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{9}{2}-\frac{1}{3}}}}{\frac{4}{5}+2}$$

Ko te maha noa iti rawa atu o 2 me 3 ko 6. Me tahuri \frac{9}{2} me \frac{1}{3} ki te hautau me te tautūnga 6.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{27}{6}-\frac{2}{6}}}}{\frac{4}{5}+2}$$

Tā te mea he rite te tauraro o \frac{27}{6} me \frac{2}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{27-2}{6}}}}{\frac{4}{5}+2}$$

Tangohia te 2 i te 27, ka 25.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{\frac{8}{3}}{\frac{25}{6}}}}{\frac{4}{5}+2}$$

Whakawehe \frac{8}{3} ki te \frac{25}{6} mā te whakarea \frac{8}{3} ki te tau huripoki o \frac{25}{6}.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{8}{3}\times \frac{6}{25}}}{\frac{4}{5}+2}$$

Me whakarea te \frac{8}{3} ki te \frac{6}{25} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{8\times 6}{3\times 25}}}{\frac{4}{5}+2}$$

Mahia ngā whakarea i roto i te hautanga \frac{8\times 6}{3\times 25}.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{48}{75}}}{\frac{4}{5}+2}$$

Whakahekea te hautanga \frac{48}{75} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{x}{\frac{7}{2}}=\frac{\sqrt{\frac{16}{25}}}{\frac{4}{5}+2}$$

Tuhia anō te pūtake rua o te whakawehenga \frac{16}{25} hei whakawehenga o ngā pūtake rua \frac{\sqrt{16}}{\sqrt{25}}. Tuhia te pūtakerua o te taurunga me te tauraro.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{4}{5}+2}$$

Me tahuri te 2 ki te hautau \frac{10}{5}.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{4}{5}+\frac{10}{5}}$$

Tā te mea he rite te tauraro o \frac{4}{5} me \frac{10}{5}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{4+10}{5}}$$

Tāpirihia te 4 ki te 10, ka 14.

$$\frac{x}{\frac{7}{2}}=\frac{\frac{4}{5}}{\frac{14}{5}}$$

Whakawehe \frac{4}{5} ki te \frac{14}{5} mā te whakarea \frac{4}{5} ki te tau huripoki o \frac{14}{5}.

$$\frac{x}{\frac{7}{2}}=\frac{4}{5}\times \frac{5}{14}$$

Me whakarea te \frac{4}{5} ki te \frac{5}{14} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{x}{\frac{7}{2}}=\frac{4\times 5}{5\times 14}$$

Me whakakore tahi te 5 i te taurunga me te tauraro.

$$\frac{x}{\frac{7}{2}}=\frac{4}{14}$$

Whakahekea te hautanga \frac{4}{14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Me whakarea ngā taha e rua ki te \frac{7}{2}.

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

Me whakakore atu te \frac{2}{7} me tōna tau utu \frac{7}{2}.

$$x=1$$