Réitigh frac{7+sqrt{6}}{7-sqrt{6}}-frac{7-sqrt{6}}{7+sqrt{6}}

$$\frac { 7 + \sqrt { 6 } } { 7 - \sqrt { 6 } } - \frac { 7 - \sqrt { 6 } } { 7 + \sqrt { 6 } }$$

Luacháil

$$\frac{28\sqrt{6}}{43}\approx 1.595016577$$

Céimeanna gearra réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 7+\sqrt{6} chun ainmneoir \frac{7+\sqrt{6}}{7-\sqrt{6}} a thiontú in uimhir chóimheasta.

$$\frac{\left(7+\sqrt{6}\right)\left(7+\sqrt{6}\right)}{\left(7-\sqrt{6}\right)\left(7+\sqrt{6}\right)}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Mar shampla \left(7-\sqrt{6}\right)\left(7+\sqrt{6}\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}.

$$\frac{\left(7+\sqrt{6}\right)\left(7+\sqrt{6}\right)}{7^{2}-\left(\sqrt{6}\right)^{2}}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Cearnóg 7. Cearnóg \sqrt{6}.

$$\frac{\left(7+\sqrt{6}\right)\left(7+\sqrt{6}\right)}{49-6}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Dealaigh 6 ó 49 chun 43 a fháil.

$$\frac{\left(7+\sqrt{6}\right)\left(7+\sqrt{6}\right)}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Méadaigh 7+\sqrt{6} agus 7+\sqrt{6} chun \left(7+\sqrt{6}\right)^{2} a fháil.

$$\frac{\left(7+\sqrt{6}\right)^{2}}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(7+\sqrt{6}\right)^{2} a leathnú.

$$\frac{49+14\sqrt{6}+\left(\sqrt{6}\right)^{2}}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Is é 6 uimhir chearnach \sqrt{6}.

$$\frac{49+14\sqrt{6}+6}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Suimigh 49 agus 6 chun 55 a fháil.

$$\frac{55+14\sqrt{6}}{43}-\frac{7-\sqrt{6}}{7+\sqrt{6}}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 7-\sqrt{6} chun ainmneoir \frac{7-\sqrt{6}}{7+\sqrt{6}} a thiontú in uimhir chóimheasta.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{\left(7+\sqrt{6}\right)\left(7-\sqrt{6}\right)}$$

Mar shampla \left(7+\sqrt{6}\right)\left(7-\sqrt{6}\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}.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{7^{2}-\left(\sqrt{6}\right)^{2}}$$

Cearnóg 7. Cearnóg \sqrt{6}.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{49-6}$$

Dealaigh 6 ó 49 chun 43 a fháil.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)\left(7-\sqrt{6}\right)}{43}$$

Méadaigh 7-\sqrt{6} agus 7-\sqrt{6} chun \left(7-\sqrt{6}\right)^{2} a fháil.

$$\frac{55+14\sqrt{6}}{43}-\frac{\left(7-\sqrt{6}\right)^{2}}{43}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(7-\sqrt{6}\right)^{2} a leathnú.

$$\frac{55+14\sqrt{6}}{43}-\frac{49-14\sqrt{6}+\left(\sqrt{6}\right)^{2}}{43}$$

Is é 6 uimhir chearnach \sqrt{6}.

$$\frac{55+14\sqrt{6}}{43}-\frac{49-14\sqrt{6}+6}{43}$$

Suimigh 49 agus 6 chun 55 a fháil.

$$\frac{55+14\sqrt{6}}{43}-\frac{55-14\sqrt{6}}{43}$$

Tá an t-ainmneoir céanna ag \frac{55+14\sqrt{6}}{43} agus \frac{55-14\sqrt{6}}{43} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{55+14\sqrt{6}-\left(55-14\sqrt{6}\right)}{43}$$

Déan iolrúcháin in 55+14\sqrt{6}-\left(55-14\sqrt{6}\right).

$$\frac{55+14\sqrt{6}-55+14\sqrt{6}}{43}$$

Déan áirimh in 55+14\sqrt{6}-55+14\sqrt{6}.

$$\frac{28\sqrt{6}}{43}$$