Issolvi frac{1/sqrt{2}-1/sqrt{3}}{1-1/sqrt{6}}

$$\frac { \frac { 1 } { \sqrt { 2 } } - \frac { 1 } { \sqrt { 3 } } } { 1 - \frac { 1 } { \sqrt { 6 } } }$$

Evalwa

$$\frac{2\sqrt{2}-\sqrt{3}}{5}\approx 0.219275263$$

Passi Qosra tas-Soluzzjonijiet

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

$$\frac{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{1}{\sqrt{3}}}{1-\frac{1}{\sqrt{6}}}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\frac{\frac{\sqrt{2}}{2}-\frac{1}{\sqrt{3}}}{1-\frac{1}{\sqrt{6}}}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\frac{\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{1-\frac{1}{\sqrt{6}}}$$

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

$$\frac{\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{3}}{1-\frac{1}{\sqrt{6}}}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 2 u 3 huwa 6. Immultiplika \frac{\sqrt{2}}{2} b'\frac{3}{3}. Immultiplika \frac{\sqrt{3}}{3} b'\frac{2}{2}.

$$\frac{\frac{3\sqrt{2}}{6}-\frac{2\sqrt{3}}{6}}{1-\frac{1}{\sqrt{6}}}$$

Billi \frac{3\sqrt{2}}{6} u \frac{2\sqrt{3}}{6} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{\frac{3\sqrt{2}-2\sqrt{3}}{6}}{1-\frac{1}{\sqrt{6}}}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{6}.

$$\frac{\frac{3\sqrt{2}-2\sqrt{3}}{6}}{1-\frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}}$$

Il-kwadrat ta' \sqrt{6} huwa 6.

$$\frac{\frac{3\sqrt{2}-2\sqrt{3}}{6}}{1-\frac{\sqrt{6}}{6}}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 1 b'\frac{6}{6}.

$$\frac{\frac{3\sqrt{2}-2\sqrt{3}}{6}}{\frac{6}{6}-\frac{\sqrt{6}}{6}}$$

Billi \frac{6}{6} u \frac{\sqrt{6}}{6} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{\frac{3\sqrt{2}-2\sqrt{3}}{6}}{\frac{6-\sqrt{6}}{6}}$$

Iddividi \frac{3\sqrt{2}-2\sqrt{3}}{6} b'\frac{6-\sqrt{6}}{6} billi timmultiplika \frac{3\sqrt{2}-2\sqrt{3}}{6} bir-reċiproku ta' \frac{6-\sqrt{6}}{6}.

$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)\times 6}{6\left(6-\sqrt{6}\right)}$$

Annulla 6 fin-numeratur u d-denominatur.

$$\frac{-2\sqrt{3}+3\sqrt{2}}{-\sqrt{6}+6}$$

Irrazzjonalizza d-denominatur tal-\frac{-2\sqrt{3}+3\sqrt{2}}{-\sqrt{6}+6} billi timmultiplika in-numeratur u d-denominatur mill--\sqrt{6}-6.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{\left(-\sqrt{6}+6\right)\left(-\sqrt{6}-6\right)}$$

Ikkunsidra li \left(-\sqrt{6}+6\right)\left(-\sqrt{6}-6\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}.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{\left(-\sqrt{6}\right)^{2}-6^{2}}$$

Espandi \left(-\sqrt{6}\right)^{2}.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{\left(-1\right)^{2}\left(\sqrt{6}\right)^{2}-6^{2}}$$

Ikkalkula -1 bil-power ta' 2 u tikseb 1.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{1\left(\sqrt{6}\right)^{2}-6^{2}}$$

Il-kwadrat ta' \sqrt{6} huwa 6.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{1\times 6-6^{2}}$$

Immultiplika 1 u 6 biex tikseb 6.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{6-6^{2}}$$

Ikkalkula 6 bil-power ta' 2 u tikseb 36.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{6-36}$$

Naqqas 36 minn 6 biex tikseb -30.

$$\frac{\left(-2\sqrt{3}+3\sqrt{2}\right)\left(-\sqrt{6}-6\right)}{-30}$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' -2\sqrt{3}+3\sqrt{2} b'kull terminu ta' -\sqrt{6}-6.

$$\frac{2\sqrt{3}\sqrt{6}+12\sqrt{3}-3\sqrt{2}\sqrt{6}-18\sqrt{2}}{-30}$$

Iffattura 6=3\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{2}.

$$\frac{2\sqrt{3}\sqrt{3}\sqrt{2}+12\sqrt{3}-3\sqrt{2}\sqrt{6}-18\sqrt{2}}{-30}$$

Immultiplika \sqrt{3} u \sqrt{3} biex tikseb 3.

$$\frac{2\times 3\sqrt{2}+12\sqrt{3}-3\sqrt{2}\sqrt{6}-18\sqrt{2}}{-30}$$

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{6\sqrt{2}+12\sqrt{3}-3\sqrt{2}\sqrt{6}-18\sqrt{2}}{-30}$$

Iffattura 6=2\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2}\sqrt{3}.

$$\frac{6\sqrt{2}+12\sqrt{3}-3\sqrt{2}\sqrt{2}\sqrt{3}-18\sqrt{2}}{-30}$$

Immultiplika \sqrt{2} u \sqrt{2} biex tikseb 2.

$$\frac{6\sqrt{2}+12\sqrt{3}-3\times 2\sqrt{3}-18\sqrt{2}}{-30}$$

Immultiplika -3 u 2 biex tikseb -6.

$$\frac{6\sqrt{2}+12\sqrt{3}-6\sqrt{3}-18\sqrt{2}}{-30}$$

Ikkombina 12\sqrt{3} u -6\sqrt{3} biex tikseb 6\sqrt{3}.

$$\frac{6\sqrt{2}+6\sqrt{3}-18\sqrt{2}}{-30}$$

Ikkombina 6\sqrt{2} u -18\sqrt{2} biex tikseb -12\sqrt{2}.

$$\frac{-12\sqrt{2}+6\sqrt{3}}{-30}$$