Issolvi frac{{left(sqrt{3}+1+sqrt{3}-1right)}^2}{{left(sqrt{3}+1right)}^2-{left(sqrt{3}-1right)}^2}

$$\frac{ { \left( \sqrt{ 3 } +1+ \sqrt{ 3 } -1 \right) }^{ 2 } }{ { \left( \sqrt{ 3 } +1 \right) }^{ 2 } - { \left( \sqrt{ 3 } -1 \right) }^{ 2 } }$$

Evalwa

$$\sqrt{3}\approx 1.732050808$$

Passi tas-Soluzzjonijiet

Ikkombina \sqrt{3} u \sqrt{3} biex tikseb 2\sqrt{3}.

$$\frac{\left(2\sqrt{3}+1-1\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Naqqas 1 minn 1 biex tikseb 0.

$$\frac{\left(2\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Espandi \left(2\sqrt{3}\right)^{2}.

$$\frac{2^{2}\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

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

$$\frac{4\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{4\times 3}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Immultiplika 4 u 3 biex tikseb 12.

$$\frac{12}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(\sqrt{3}+1\right)^{2}.

$$\frac{12}{\left(\sqrt{3}\right)^{2}+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{12}{3+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Żid 3 u 1 biex tikseb 4.

$$\frac{12}{4+2\sqrt{3}-\left(\sqrt{3}-1\right)^{2}}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(\sqrt{3}-1\right)^{2}.

$$\frac{12}{4+2\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1\right)}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{12}{4+2\sqrt{3}-\left(3-2\sqrt{3}+1\right)}$$

Żid 3 u 1 biex tikseb 4.

$$\frac{12}{4+2\sqrt{3}-\left(4-2\sqrt{3}\right)}$$

Biex issib l-oppost ta' 4-2\sqrt{3}, sib l-oppost ta' kull terminu.

$$\frac{12}{4+2\sqrt{3}-4+2\sqrt{3}}$$

Naqqas 4 minn 4 biex tikseb 0.

$$\frac{12}{2\sqrt{3}+2\sqrt{3}}$$

Ikkombina 2\sqrt{3} u 2\sqrt{3} biex tikseb 4\sqrt{3}.

$$\frac{12}{4\sqrt{3}}$$

Irrazzjonalizza d-denominatur tal-\frac{12}{4\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\frac{12\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{12\sqrt{3}}{4\times 3}$$

Annulla 3\times 4 fin-numeratur u d-denominatur.

$$\sqrt{3}$$

Espandi

$$\sqrt{3} = 1.732050808$$

Passi tas-Soluzzjonijiet

Ikkombina \sqrt{3} u \sqrt{3} biex tikseb 2\sqrt{3}.

$$\frac{\left(2\sqrt{3}+1-1\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Naqqas 1 minn 1 biex tikseb 0.

$$\frac{\left(2\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Espandi \left(2\sqrt{3}\right)^{2}.

$$\frac{2^{2}\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

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

$$\frac{4\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{4\times 3}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Immultiplika 4 u 3 biex tikseb 12.

$$\frac{12}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(\sqrt{3}+1\right)^{2}.

$$\frac{12}{\left(\sqrt{3}\right)^{2}+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{12}{3+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Żid 3 u 1 biex tikseb 4.

$$\frac{12}{4+2\sqrt{3}-\left(\sqrt{3}-1\right)^{2}}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(\sqrt{3}-1\right)^{2}.

$$\frac{12}{4+2\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1\right)}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{12}{4+2\sqrt{3}-\left(3-2\sqrt{3}+1\right)}$$

Żid 3 u 1 biex tikseb 4.

$$\frac{12}{4+2\sqrt{3}-\left(4-2\sqrt{3}\right)}$$

Biex issib l-oppost ta' 4-2\sqrt{3}, sib l-oppost ta' kull terminu.

$$\frac{12}{4+2\sqrt{3}-4+2\sqrt{3}}$$

Naqqas 4 minn 4 biex tikseb 0.

$$\frac{12}{2\sqrt{3}+2\sqrt{3}}$$

Ikkombina 2\sqrt{3} u 2\sqrt{3} biex tikseb 4\sqrt{3}.

$$\frac{12}{4\sqrt{3}}$$

Irrazzjonalizza d-denominatur tal-\frac{12}{4\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\frac{12\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{12\sqrt{3}}{4\times 3}$$

Annulla 3\times 4 fin-numeratur u d-denominatur.

$$\sqrt{3}$$