Whakaoti i te 3/sqrt{5}-frac{2+sqrt{5}}{3sqrt{5}-5}

$$\frac{ 3 }{ \sqrt{ 5 } } - \frac{ 2+ \sqrt{ 5 } }{ 3 \sqrt{ 5 } -5 }$$

Aromātai

$$\frac{\sqrt{5}-25}{20}\approx -1.138196601$$

Ngā Hipanga Rongoā Poto

Whakangāwaritia te tauraro o \frac{3}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{3\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-\frac{2+\sqrt{5}}{3\sqrt{5}-5}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{3\sqrt{5}}{5}-\frac{2+\sqrt{5}}{3\sqrt{5}-5}$$

Whakangāwaritia te tauraro o \frac{2+\sqrt{5}}{3\sqrt{5}-5} mā te whakarea i te taurunga me te tauraro ki te 3\sqrt{5}+5.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{\left(3\sqrt{5}-5\right)\left(3\sqrt{5}+5\right)}$$

Whakaarohia te \left(3\sqrt{5}-5\right)\left(3\sqrt{5}+5\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}.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{\left(3\sqrt{5}\right)^{2}-5^{2}}$$

Whakarohaina te \left(3\sqrt{5}\right)^{2}.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{3^{2}\left(\sqrt{5}\right)^{2}-5^{2}}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{9\left(\sqrt{5}\right)^{2}-5^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{9\times 5-5^{2}}$$

Whakareatia te 9 ki te 5, ka 45.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{45-5^{2}}$$

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{45-25}$$

Tangohia te 25 i te 45, ka 20.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 5 me 20 ko 20. Whakareatia \frac{3\sqrt{5}}{5} ki te \frac{4}{4}.

$$\frac{4\times 3\sqrt{5}}{20}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20}$$

Tā te mea he rite te tauraro o \frac{4\times 3\sqrt{5}}{20} me \frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{4\times 3\sqrt{5}-\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20}$$

Mahia ngā whakarea i roto o 4\times 3\sqrt{5}-\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right).

$$\frac{12\sqrt{5}-6\sqrt{5}-10-15-5\sqrt{5}}{20}$$

Mahia ngā tātaitai i roto o 12\sqrt{5}-6\sqrt{5}-10-15-5\sqrt{5}.

$$\frac{\sqrt{5}-25}{20}$$