Réitigh 3/sqrt{5}-frac{2+sqrt{5}}{3sqrt{5}-5}

$$\frac{ 3 }{ \sqrt{ 5 } } - \frac{ 2+ \sqrt{ 5 } }{ 3 \sqrt{ 5 } -5 }$$

Luacháil

$$\frac{\sqrt{5}-25}{20}\approx -1.138196601$$

Céimeanna gearra réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{5} chun ainmneoir \frac{3}{\sqrt{5}} a thiontú in uimhir chóimheasta.

$$\frac{3\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-\frac{2+\sqrt{5}}{3\sqrt{5}-5}$$

Is é 5 uimhir chearnach \sqrt{5}.

$$\frac{3\sqrt{5}}{5}-\frac{2+\sqrt{5}}{3\sqrt{5}-5}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 3\sqrt{5}+5 chun ainmneoir \frac{2+\sqrt{5}}{3\sqrt{5}-5} a thiontú in uimhir chóimheasta.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{\left(3\sqrt{5}-5\right)\left(3\sqrt{5}+5\right)}$$

Mar shampla \left(3\sqrt{5}-5\right)\left(3\sqrt{5}+5\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}.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{\left(3\sqrt{5}\right)^{2}-5^{2}}$$

Fairsingigh \left(3\sqrt{5}\right)^{2}

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{3^{2}\left(\sqrt{5}\right)^{2}-5^{2}}$$

Ríomh cumhacht 3 de 2 agus faigh 9.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{9\left(\sqrt{5}\right)^{2}-5^{2}}$$

Is é 5 uimhir chearnach \sqrt{5}.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{9\times 5-5^{2}}$$

Méadaigh 9 agus 5 chun 45 a fháil.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{45-5^{2}}$$

Ríomh cumhacht 5 de 2 agus faigh 25.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{45-25}$$

Dealaigh 25 ó 45 chun 20 a fháil.

$$\frac{3\sqrt{5}}{5}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de 5 agus 20 ná 20. Méadaigh \frac{3\sqrt{5}}{5} faoi \frac{4}{4}.

$$\frac{4\times 3\sqrt{5}}{20}-\frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20}$$

Tá an t-ainmneoir céanna ag \frac{4\times 3\sqrt{5}}{20} agus \frac{\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{4\times 3\sqrt{5}-\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right)}{20}$$

Déan iolrúcháin in 4\times 3\sqrt{5}-\left(2+\sqrt{5}\right)\left(3\sqrt{5}+5\right).

$$\frac{12\sqrt{5}-6\sqrt{5}-10-15-5\sqrt{5}}{20}$$

Déan áirimh in 12\sqrt{5}-6\sqrt{5}-10-15-5\sqrt{5}.

$$\frac{\sqrt{5}-25}{20}$$