Réitigh frac{1/sqrt{2}-1}{1/sqrt{2}+sqrt{3}}

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

Luacháil

$$\frac{\sqrt{2}+\sqrt{6}-2\sqrt{3}-1}{5}\approx -0.120079662$$

Céimeanna gearra réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2} chun ainmneoir \frac{1}{\sqrt{2}} a thiontú in uimhir chóimheasta.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh 1 faoi \frac{2}{2}.

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

Tá an t-ainmneoir céanna ag \frac{\sqrt{2}}{2} agus \frac{2}{2} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2} chun ainmneoir \frac{1}{\sqrt{2}} a thiontú in uimhir chóimheasta.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh \sqrt{3} faoi \frac{2}{2}.

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

Tá an t-ainmneoir céanna ag \frac{\sqrt{2}}{2} agus \frac{2\sqrt{3}}{2} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

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

Roinn \frac{\sqrt{2}-2}{2} faoi \frac{\sqrt{2}+2\sqrt{3}}{2} trí \frac{\sqrt{2}-2}{2} a mhéadú faoi dheilín \frac{\sqrt{2}+2\sqrt{3}}{2}.

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

Cealaigh 2 mar uimhreoir agus ainmneoir.

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

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2}-2\sqrt{3} chun ainmneoir \frac{\sqrt{2}-2}{\sqrt{2}+2\sqrt{3}} a thiontú in uimhir chóimheasta.

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

Mar shampla \left(\sqrt{2}+2\sqrt{3}\right)\left(\sqrt{2}-2\sqrt{3}\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Fairsingigh \left(2\sqrt{3}\right)^{2}

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

Ríomh cumhacht 2 de 2 agus faigh 4.

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

Is é 3 uimhir chearnach \sqrt{3}.

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

Méadaigh 4 agus 3 chun 12 a fháil.

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

Dealaigh 12 ó 2 chun -10 a fháil.

$$\frac{\left(\sqrt{2}-2\right)\left(\sqrt{2}-2\sqrt{3}\right)}{-10}$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de \sqrt{2}-2 a iolrú faoi gach téarma de \sqrt{2}-2\sqrt{3}.

$$\frac{\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}-2\sqrt{2}+4\sqrt{3}}{-10}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{2-2\sqrt{2}\sqrt{3}-2\sqrt{2}+4\sqrt{3}}{-10}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{2} agus \sqrt{3} a iolrú.

$$\frac{2-2\sqrt{6}-2\sqrt{2}+4\sqrt{3}}{-10}$$