Réitigh sqrt{2}+1-frac{1+sqrt{2}}{sqrt{2}+156}

$$\sqrt{ 2 } +1- \frac{ 1+ \sqrt{ 2 } }{ \sqrt{ 2 } +156 }$$

Luacháil

$$\frac{24179\sqrt{2}}{24334}+\frac{12090}{12167}\approx 2.398876869$$

Céimeanna gearra réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2}-156 chun ainmneoir \frac{1+\sqrt{2}}{\sqrt{2}+156} a thiontú in uimhir chóimheasta.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{\left(\sqrt{2}+156\right)\left(\sqrt{2}-156\right)}$$

Mar shampla \left(\sqrt{2}+156\right)\left(\sqrt{2}-156\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}.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{\left(\sqrt{2}\right)^{2}-156^{2}}$$

Cearnóg \sqrt{2}. Cearnóg 156.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{2-24336}$$

Dealaigh 24336 ó 2 chun -24334 a fháil.

$$\sqrt{2}+1-\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}-156\right)}{-24334}$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de 1+\sqrt{2} a iolrú faoi gach téarma de \sqrt{2}-156.

$$\sqrt{2}+1-\frac{\sqrt{2}-156+\left(\sqrt{2}\right)^{2}-156\sqrt{2}}{-24334}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$\sqrt{2}+1-\frac{\sqrt{2}-156+2-156\sqrt{2}}{-24334}$$

Suimigh -156 agus 2 chun -154 a fháil.

$$\sqrt{2}+1-\frac{\sqrt{2}-154-156\sqrt{2}}{-24334}$$

Comhcheangail \sqrt{2} agus -156\sqrt{2} chun -155\sqrt{2} a fháil.

$$\sqrt{2}+1-\frac{-155\sqrt{2}-154}{-24334}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi -1.

$$\sqrt{2}+1-\frac{155\sqrt{2}+154}{24334}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh \sqrt{2}+1 faoi \frac{24334}{24334}.

$$\frac{24334\left(\sqrt{2}+1\right)}{24334}-\frac{155\sqrt{2}+154}{24334}$$

Tá an t-ainmneoir céanna ag \frac{24334\left(\sqrt{2}+1\right)}{24334} agus \frac{155\sqrt{2}+154}{24334} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{24334\left(\sqrt{2}+1\right)-\left(155\sqrt{2}+154\right)}{24334}$$

Déan iolrúcháin in 24334\left(\sqrt{2}+1\right)-\left(155\sqrt{2}+154\right).

$$\frac{24334\sqrt{2}[phone]\sqrt{2}-154}{24334}$$

Déan áirimh in 24334\sqrt{2}[phone]\sqrt{2}-154.

$$\frac{24179\sqrt{2}+24180}{24334}$$