Whakaoti i te frac{1-4sqrt{5}-3}{3-sqrt{5}-sqrt{5}+2}=

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

Aromātai

$$-\frac{24\sqrt{5}}{5}-10\approx -20.733126292$$

Ngā Upane Otinga

Tangohia te 3 i te 1, ka -2.

$$\frac{-2-4\sqrt{5}}{3-\sqrt{5}-\sqrt{5}+2}$$

Pahekotia te -\sqrt{5} me -\sqrt{5}, ka -2\sqrt{5}.

$$\frac{-2-4\sqrt{5}}{3-2\sqrt{5}+2}$$

Tāpirihia te 3 ki te 2, ka 5.

$$\frac{-2-4\sqrt{5}}{5-2\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{-2-4\sqrt{5}}{5-2\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te 5+2\sqrt{5}.

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

Whakaarohia te \left(5-2\sqrt{5}\right)\left(5+2\sqrt{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}.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{5^{2}-\left(-2\sqrt{5}\right)^{2}}$$

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

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-\left(-2\sqrt{5}\right)^{2}}$$

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

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-\left(-2\right)^{2}\left(\sqrt{5}\right)^{2}}$$

Tātaihia te -2 mā te pū o 2, kia riro ko 4.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-4\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-4\times 5}$$

Whakareatia te 4 ki te 5, ka 20.

$$\frac{\left(-2-4\sqrt{5}\right)\left(5+2\sqrt{5}\right)}{25-20}$$

Tangohia te 20 i te 25, ka 5.

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

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o -2-4\sqrt{5} ki ia tau o 5+2\sqrt{5}.

$$\frac{-10-4\sqrt{5}-20\sqrt{5}-8\left(\sqrt{5}\right)^{2}}{5}$$

Pahekotia te -4\sqrt{5} me -20\sqrt{5}, ka -24\sqrt{5}.

$$\frac{-10-24\sqrt{5}-8\left(\sqrt{5}\right)^{2}}{5}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{-10-24\sqrt{5}-8\times 5}{5}$$

Whakareatia te -8 ki te 5, ka -40.

$$\frac{-10-24\sqrt{5}-40}{5}$$

Tangohia te 40 i te -10, ka -50.

$$\frac{-50-24\sqrt{5}}{5}$$