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

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

Evalwa

$$-2$$

Passi Qosra tas-Soluzzjonijiet

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

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

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}.

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

Ikkwadra -2. Ikkwadra \sqrt{2}.

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

Naqqas 2 minn 4 biex tikseb 2.

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

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

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

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}.

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

Ikkwadra -2. Ikkwadra \sqrt{2}.

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

Naqqas 2 minn 4 biex tikseb 2.

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

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

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

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

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

Iddividi -4 b'2 biex tikseb-2.

$$-2$$

Fattur

$$-2$$