Réitigh frac{4-sqrt{2}}{4+sqrt{2}}-frac{4+sqrt{2}}{4-sqrt{2}}

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

Luacháil

$$-\frac{8\sqrt{2}}{7}\approx -1.616244071$$

Céimeanna gearra réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 4-\sqrt{2} chun ainmneoir \frac{4-\sqrt{2}}{4+\sqrt{2}} a thiontú in uimhir chóimheasta.

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

Mar shampla \left(4+\sqrt{2}\right)\left(4-\sqrt{2}\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}.

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

Cearnóg 4. Cearnóg \sqrt{2}.

$$\frac{\left(4-\sqrt{2}\right)\left(4-\sqrt{2}\right)}{16-2}-\frac{4+\sqrt{2}}{4-\sqrt{2}}$$

Dealaigh 2 ó 16 chun 14 a fháil.

$$\frac{\left(4-\sqrt{2}\right)\left(4-\sqrt{2}\right)}{14}-\frac{4+\sqrt{2}}{4-\sqrt{2}}$$

Méadaigh 4-\sqrt{2} agus 4-\sqrt{2} chun \left(4-\sqrt{2}\right)^{2} a fháil.

$$\frac{\left(4-\sqrt{2}\right)^{2}}{14}-\frac{4+\sqrt{2}}{4-\sqrt{2}}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(4-\sqrt{2}\right)^{2} a leathnú.

$$\frac{16-8\sqrt{2}+\left(\sqrt{2}\right)^{2}}{14}-\frac{4+\sqrt{2}}{4-\sqrt{2}}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{16-8\sqrt{2}+2}{14}-\frac{4+\sqrt{2}}{4-\sqrt{2}}$$

Suimigh 16 agus 2 chun 18 a fháil.

$$\frac{18-8\sqrt{2}}{14}-\frac{4+\sqrt{2}}{4-\sqrt{2}}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 4+\sqrt{2} chun ainmneoir \frac{4+\sqrt{2}}{4-\sqrt{2}} a thiontú in uimhir chóimheasta.

$$\frac{18-8\sqrt{2}}{14}-\frac{\left(4+\sqrt{2}\right)\left(4+\sqrt{2}\right)}{\left(4-\sqrt{2}\right)\left(4+\sqrt{2}\right)}$$

Mar shampla \left(4-\sqrt{2}\right)\left(4+\sqrt{2}\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}.

$$\frac{18-8\sqrt{2}}{14}-\frac{\left(4+\sqrt{2}\right)\left(4+\sqrt{2}\right)}{4^{2}-\left(\sqrt{2}\right)^{2}}$$

Cearnóg 4. Cearnóg \sqrt{2}.

$$\frac{18-8\sqrt{2}}{14}-\frac{\left(4+\sqrt{2}\right)\left(4+\sqrt{2}\right)}{16-2}$$

Dealaigh 2 ó 16 chun 14 a fháil.

$$\frac{18-8\sqrt{2}}{14}-\frac{\left(4+\sqrt{2}\right)\left(4+\sqrt{2}\right)}{14}$$

Méadaigh 4+\sqrt{2} agus 4+\sqrt{2} chun \left(4+\sqrt{2}\right)^{2} a fháil.

$$\frac{18-8\sqrt{2}}{14}-\frac{\left(4+\sqrt{2}\right)^{2}}{14}$$

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(4+\sqrt{2}\right)^{2} a leathnú.

$$\frac{18-8\sqrt{2}}{14}-\frac{16+8\sqrt{2}+\left(\sqrt{2}\right)^{2}}{14}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\frac{18-8\sqrt{2}}{14}-\frac{16+8\sqrt{2}+2}{14}$$

Suimigh 16 agus 2 chun 18 a fháil.

$$\frac{18-8\sqrt{2}}{14}-\frac{18+8\sqrt{2}}{14}$$

Tá an t-ainmneoir céanna ag \frac{18-8\sqrt{2}}{14} agus \frac{18+8\sqrt{2}}{14} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{18-8\sqrt{2}-\left(18+8\sqrt{2}\right)}{14}$$

Déan iolrúcháin in 18-8\sqrt{2}-\left(18+8\sqrt{2}\right).

$$\frac{18-8\sqrt{2}-18-8\sqrt{2}}{14}$$

Déan áirimh in 18-8\sqrt{2}-18-8\sqrt{2}.

$$\frac{-16\sqrt{2}}{14}$$

Roinn -16\sqrt{2} faoi 14 chun -\frac{8}{7}\sqrt{2} a fháil.

$$-\frac{8}{7}\sqrt{2}$$