Whakaoti i te frac{frac{sqrt{3}}{2}-154/308^2}{frac{sqrt{3}}{2}+154/308^2}

$$\frac{ \frac{ \sqrt{ 3 } }{ 2 } - \frac{ 154 }{ { 308 }^{ 2 } } }{ \frac{ \sqrt{ 3 } }{ 2 } + \frac{ 154 }{ { 308 }^{ 2 } } }$$

Aromātai

$$\frac{284593-616\sqrt{3}}{284591}\approx 0.996257987$$

Ngā Hipanga Rongoā Poto

Tātaihia te 308 mā te pū o 2, kia riro ko 94864.

$$\frac{\frac{\sqrt{3}}{2}-\frac{154}{94864}}{\frac{\sqrt{3}}{2}+\frac{154}{308^{2}}}$$

Whakahekea te hautanga \frac{154}{94864} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 154.

$$\frac{\frac{\sqrt{3}}{2}-\frac{1}{616}}{\frac{\sqrt{3}}{2}+\frac{154}{308^{2}}}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2 me 616 ko 616. Whakareatia \frac{\sqrt{3}}{2} ki te \frac{308}{308}.

$$\frac{\frac{308\sqrt{3}}{616}-\frac{1}{616}}{\frac{\sqrt{3}}{2}+\frac{154}{308^{2}}}$$

Tā te mea he rite te tauraro o \frac{308\sqrt{3}}{616} me \frac{1}{616}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{308\sqrt{3}-1}{616}}{\frac{\sqrt{3}}{2}+\frac{154}{308^{2}}}$$

Tātaihia te 308 mā te pū o 2, kia riro ko 94864.

$$\frac{\frac{308\sqrt{3}-1}{616}}{\frac{\sqrt{3}}{2}+\frac{154}{94864}}$$

Whakahekea te hautanga \frac{154}{94864} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 154.

$$\frac{\frac{308\sqrt{3}-1}{616}}{\frac{\sqrt{3}}{2}+\frac{1}{616}}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2 me 616 ko 616. Whakareatia \frac{\sqrt{3}}{2} ki te \frac{308}{308}.

$$\frac{\frac{308\sqrt{3}-1}{616}}{\frac{308\sqrt{3}}{616}+\frac{1}{616}}$$

Tā te mea he rite te tauraro o \frac{308\sqrt{3}}{616} me \frac{1}{616}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{308\sqrt{3}-1}{616}}{\frac{308\sqrt{3}+1}{616}}$$

Whakawehe \frac{308\sqrt{3}-1}{616} ki te \frac{308\sqrt{3}+1}{616} mā te whakarea \frac{308\sqrt{3}-1}{616} ki te tau huripoki o \frac{308\sqrt{3}+1}{616}.

$$\frac{\left(308\sqrt{3}-1\right)\times 616}{616\left(308\sqrt{3}+1\right)}$$

Me whakakore tahi te 616 i te taurunga me te tauraro.

$$\frac{308\sqrt{3}-1}{308\sqrt{3}+1}$$

Whakangāwaritia te tauraro o \frac{308\sqrt{3}-1}{308\sqrt{3}+1} mā te whakarea i te taurunga me te tauraro ki te 308\sqrt{3}-1.

$$\frac{\left(308\sqrt{3}-1\right)\left(308\sqrt{3}-1\right)}{\left(308\sqrt{3}+1\right)\left(308\sqrt{3}-1\right)}$$

Whakaarohia te \left(308\sqrt{3}+1\right)\left(308\sqrt{3}-1\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(308\sqrt{3}-1\right)\left(308\sqrt{3}-1\right)}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Whakareatia te 308\sqrt{3}-1 ki te 308\sqrt{3}-1, ka \left(308\sqrt{3}-1\right)^{2}.

$$\frac{\left(308\sqrt{3}-1\right)^{2}}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(308\sqrt{3}-1\right)^{2}.

$$\frac{94864\left(\sqrt{3}\right)^{2}-616\sqrt{3}+1}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{94864\times 3-616\sqrt{3}+1}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Whakareatia te 94864 ki te 3, ka 284592.

$$\frac{284592-616\sqrt{3}+1}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Tāpirihia te 284592 ki te 1, ka 284593.

$$\frac{284593-616\sqrt{3}}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Whakarohaina te \left(308\sqrt{3}\right)^{2}.

$$\frac{284593-616\sqrt{3}}{308^{2}\left(\sqrt{3}\right)^{2}-1^{2}}$$

Tātaihia te 308 mā te pū o 2, kia riro ko 94864.

$$\frac{284593-616\sqrt{3}}{94864\left(\sqrt{3}\right)^{2}-1^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{284593-616\sqrt{3}}{94864\times 3-1^{2}}$$

Whakareatia te 94864 ki te 3, ka 284592.

$$\frac{284593-616\sqrt{3}}{284592-1^{2}}$$

Tātaihia te 1 mā te pū o 2, kia riro ko 1.

$$\frac{284593-616\sqrt{3}}{284592-1}$$

Tangohia te 1 i te 284592, ka 284591.

$$\frac{284593-616\sqrt{3}}{284591}$$

Tauwehe

$$\frac{284593 - 616 \sqrt{3}}{284591} = 0.9962579867337251$$