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

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

Luacháil

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

Céimeanna Réitigh

Dealaigh 3 ó 1 chun -2 a fháil.

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

Comhcheangail -\sqrt{5} agus -\sqrt{5} chun -2\sqrt{5} a fháil.

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

Suimigh 3 agus 2 chun 5 a fháil.

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

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 5+2\sqrt{5} chun ainmneoir \frac{-2-4\sqrt{5}}{5-2\sqrt{5}} a thiontú in uimhir chóimheasta.

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

Mar shampla \left(5-2\sqrt{5}\right)\left(5+2\sqrt{5}\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ríomh cumhacht 5 de 2 agus faigh 25.

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

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

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

Ríomh cumhacht -2 de 2 agus faigh 4.

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

Is é 5 uimhir chearnach \sqrt{5}.

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

Méadaigh 4 agus 5 chun 20 a fháil.

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

Dealaigh 20 ó 25 chun 5 a fháil.

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

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de -2-4\sqrt{5} a iolrú faoi gach téarma de 5+2\sqrt{5}.

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

Comhcheangail -4\sqrt{5} agus -20\sqrt{5} chun -24\sqrt{5} a fháil.

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

Is é 5 uimhir chearnach \sqrt{5}.

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

Méadaigh -8 agus 5 chun -40 a fháil.

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

Dealaigh 40 ó -10 chun -50 a fháil.

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