Issolvi 1/2-sqrt{2}+1/sqrt{2-1}):1/2

$$\frac { 1 } { 2 - \sqrt { 2 } } + \frac { 1 } { \sqrt { 2 } - 1 } ) : \frac { 1 } { 2 }$$

Evalwa

$$\frac{3\sqrt{2}}{2}+2\approx 4.121320344$$

Passi Qosra tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{1}{2-\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-2+\sqrt{2}.

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

Ikkunsidra li \left(2-\sqrt{2}\right)\left(2+\sqrt{2}\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}.

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

Ikkwadra 2. Ikkwadra \sqrt{2}.

$$\frac{2+\sqrt{2}}{4-2}+\frac{1}{\sqrt{2}-1}$$

Naqqas 2 minn 4 biex tikseb 2.

$$\frac{2+\sqrt{2}}{2}+\frac{1}{\sqrt{2}-1}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{2}-1} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}+1.

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

Ikkunsidra li \left(\sqrt{2}-1\right)\left(\sqrt{2}+1\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}.

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

Ikkwadra \sqrt{2}. Ikkwadra 1.

$$\frac{2+\sqrt{2}}{2}+\frac{\sqrt{2}+1}{2-1}$$

Naqqas 1 minn 2 biex tikseb 1.

$$\frac{2+\sqrt{2}}{2}+\frac{\sqrt{2}+1}{1}$$

Kwalunkwe ħaġa diviża b'wieħed tagħti riżultat tagħha stess.

$$\frac{2+\sqrt{2}}{2}+\sqrt{2}+1$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika \sqrt{2}+1 b'\frac{2}{2}.

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

Billi \frac{2+\sqrt{2}}{2} u \frac{2\left(\sqrt{2}+1\right)}{2} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi 2+\sqrt{2}+2\left(\sqrt{2}+1\right).

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

Agħmel il-kalkoli fi 2+\sqrt{2}+2\sqrt{2}+2.

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