Whakaoti i te 5-7/5/frac{24{7}sqrt{2}}=x/5+frac{7{5}}

$$\frac { 5 - \frac { 7 } { 5 } } { \frac { 24 } { 7 } \sqrt { 2 } } = \frac { x } { 5 + \frac { 7 } { 5 } }$$

Whakaoti mō x

$$x = \frac{84 \sqrt{2}}{25} \approx 4.75175757$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me tahuri te 5 ki te hautau \frac{25}{5}.

$$\frac{\frac{25}{5}-\frac{7}{5}}{\frac{24}{7}\sqrt{2}}=\frac{x}{5+\frac{7}{5}}$$

Tā te mea he rite te tauraro o \frac{25}{5} me \frac{7}{5}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{25-7}{5}}{\frac{24}{7}\sqrt{2}}=\frac{x}{5+\frac{7}{5}}$$

Tangohia te 7 i te 25, ka 18.

$$\frac{\frac{18}{5}}{\frac{24}{7}\sqrt{2}}=\frac{x}{5+\frac{7}{5}}$$

Tuhia te \frac{\frac{18}{5}}{\frac{24}{7}\sqrt{2}} hei hautanga kotahi.

$$\frac{18}{5\times \frac{24}{7}\sqrt{2}}=\frac{x}{5+\frac{7}{5}}$$

Whakangāwaritia te tauraro o \frac{18}{5\times \frac{24}{7}\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{18\sqrt{2}}{5\times \frac{24}{7}\left(\sqrt{2}\right)^{2}}=\frac{x}{5+\frac{7}{5}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{18\sqrt{2}}{5\times \frac{24}{7}\times 2}=\frac{x}{5+\frac{7}{5}}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$\frac{9\sqrt{2}}{\frac{24}{7}\times 5}=\frac{x}{5+\frac{7}{5}}$$

Tuhia te \frac{24}{7}\times 5 hei hautanga kotahi.

$$\frac{9\sqrt{2}}{\frac{24\times 5}{7}}=\frac{x}{5+\frac{7}{5}}$$

Whakareatia te 24 ki te 5, ka 120.

$$\frac{9\sqrt{2}}{\frac{120}{7}}=\frac{x}{5+\frac{7}{5}}$$

Whakawehea te 9\sqrt{2} ki te \frac{120}{7}, kia riro ko \frac{21}{40}\sqrt{2}.

$$\frac{21}{40}\sqrt{2}=\frac{x}{5+\frac{7}{5}}$$

Me tahuri te 5 ki te hautau \frac{25}{5}.

$$\frac{21}{40}\sqrt{2}=\frac{x}{\frac{25}{5}+\frac{7}{5}}$$

Tā te mea he rite te tauraro o \frac{25}{5} me \frac{7}{5}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{21}{40}\sqrt{2}=\frac{x}{\frac{25+7}{5}}$$

Tāpirihia te 25 ki te 7, ka 32.

$$\frac{21}{40}\sqrt{2}=\frac{x}{\frac{32}{5}}$$

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

$$\frac{x}{\frac{32}{5}}=\frac{21}{40}\sqrt{2}$$

He hanga arowhānui tō te whārite.

$$\frac{5}{32}x=\frac{21\sqrt{2}}{40}$$

Whakawehea ngā taha e rua o te whārite ki te \frac{5}{32}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{\frac{5}{32}x}{\frac{5}{32}}=\frac{21\sqrt{2}}{\frac{5}{32}\times 40}$$

Mā te whakawehe ki te \frac{5}{32} ka wetekia te whakareanga ki te \frac{5}{32}.

$$x=\frac{21\sqrt{2}}{\frac{5}{32}\times 40}$$

Whakawehe \frac{21\sqrt{2}}{40} ki te \frac{5}{32} mā te whakarea \frac{21\sqrt{2}}{40} ki te tau huripoki o \frac{5}{32}.

$$x=\frac{84\sqrt{2}}{25}$$