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

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

Enrhifo

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

Camau Ateb

Tynnu 3 o 1 i gael -2.

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

Cyfuno -\sqrt{5} a -\sqrt{5} i gael -2\sqrt{5}.

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

Adio 3 a 2 i gael 5.

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

Mae'n rhesymoli enwadur \frac{-2-4\sqrt{5}}{5-2\sqrt{5}} drwy luosi'r rhifiadur a'r enwadur â 5+2\sqrt{5}.

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

Ystyriwch \left(5-2\sqrt{5}\right)\left(5+2\sqrt{5}\right). Gellir trawsnewid lluosi yn wahaniaeth rhwng sgwariau drwy ddefnyddio’r rheol: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Cyfrifo 5 i bŵer 2 a chael 25.

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

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

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

Cyfrifo -2 i bŵer 2 a chael 4.

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

Sgwâr \sqrt{5} yw 5.

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

Lluosi 4 a 5 i gael 20.

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

Tynnu 20 o 25 i gael 5.

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

Cyfrifwch y briodoledd ddosrannol drwy luosi pob -2-4\sqrt{5} gan bob 5+2\sqrt{5}.

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

Cyfuno -4\sqrt{5} a -20\sqrt{5} i gael -24\sqrt{5}.

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

Sgwâr \sqrt{5} yw 5.

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

Lluosi -8 a 5 i gael -40.

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

Tynnu 40 o -10 i gael -50.

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