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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Naqqas 3 minn 1 biex tikseb -2.

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

Ikkombina -\sqrt{5} u -\sqrt{5} biex tikseb -2\sqrt{5}.

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

Żid 3 u 2 biex tikseb 5.

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

Irrazzjonalizza d-denominatur tal-\frac{-2-4\sqrt{5}}{5-2\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-5+2\sqrt{5}.

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

Ikkunsidra li \left(5-2\sqrt{5}\right)\left(5+2\sqrt{5}\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ikkalkula 5 bil-power ta' 2 u tikseb 25.

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

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

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

Ikkalkula -2 bil-power ta' 2 u tikseb 4.

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

Il-kwadrat ta' \sqrt{5} huwa 5.

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

Immultiplika 4 u 5 biex tikseb 20.

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

Naqqas 20 minn 25 biex tikseb 5.

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

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' -2-4\sqrt{5} b'kull terminu ta' 5+2\sqrt{5}.

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

Ikkombina -4\sqrt{5} u -20\sqrt{5} biex tikseb -24\sqrt{5}.

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

Il-kwadrat ta' \sqrt{5} huwa 5.

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

Immultiplika -8 u 5 biex tikseb -40.

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

Naqqas 40 minn -10 biex tikseb -50.

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