Lahenda 300-frac{700/sqrt{109}}{650+210/sqrt{109}}

$$\frac{ 300- \frac{ 700 }{ \sqrt{ 109 } } }{ 650+ \frac{ 210 }{ \sqrt{ 109 } } }$$

Arvuta

$$\frac{53505-1295\sqrt{109}}{115021}\approx 0,347630459$$

Lühike lahenduskäik

Ratsionaliseerige korrutades lugeja ja \sqrt{109} nimetaja \frac{700}{\sqrt{109}} nimetaja.

$$\frac{300-\frac{700\sqrt{109}}{\left(\sqrt{109}\right)^{2}}}{650+\frac{210}{\sqrt{109}}}$$

\sqrt{109} ruut on 109.

$$\frac{300-\frac{700\sqrt{109}}{109}}{650+\frac{210}{\sqrt{109}}}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 300 ja \frac{109}{109}.

$$\frac{\frac{300\times 109}{109}-\frac{700\sqrt{109}}{109}}{650+\frac{210}{\sqrt{109}}}$$

Kuna murdudel \frac{300\times 109}{109} ja \frac{700\sqrt{109}}{109} on sama nimetaja, lahutage nende lugejad.

$$\frac{\frac{300\times 109-700\sqrt{109}}{109}}{650+\frac{210}{\sqrt{109}}}$$

Tehke korrutustehted võrrandis 300\times 109-700\sqrt{109}.

$$\frac{\frac{32700-700\sqrt{109}}{109}}{650+\frac{210}{\sqrt{109}}}$$

Ratsionaliseerige korrutades lugeja ja \sqrt{109} nimetaja \frac{210}{\sqrt{109}} nimetaja.

$$\frac{\frac{32700-700\sqrt{109}}{109}}{650+\frac{210\sqrt{109}}{\left(\sqrt{109}\right)^{2}}}$$

\sqrt{109} ruut on 109.

$$\frac{\frac{32700-700\sqrt{109}}{109}}{650+\frac{210\sqrt{109}}{109}}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 650 ja \frac{109}{109}.

$$\frac{\frac{32700-700\sqrt{109}}{109}}{\frac{650\times 109}{109}+\frac{210\sqrt{109}}{109}}$$

Kuna murdudel \frac{650\times 109}{109} ja \frac{210\sqrt{109}}{109} on sama nimetaja, liitke nende lugejad.

$$\frac{\frac{32700-700\sqrt{109}}{109}}{\frac{650\times 109+210\sqrt{109}}{109}}$$

Tehke korrutustehted võrrandis 650\times 109+210\sqrt{109}.

$$\frac{\frac{32700-700\sqrt{109}}{109}}{\frac{70850+210\sqrt{109}}{109}}$$

Jagage \frac{32700-700\sqrt{109}}{109} väärtusega \frac{70850+210\sqrt{109}}{109}, korrutades \frac{32700-700\sqrt{109}}{109} väärtuse \frac{70850+210\sqrt{109}}{109} pöördväärtusega.

$$\frac{\left(32700-700\sqrt{109}\right)\times 109}{109\left(70850+210\sqrt{109}\right)}$$

Taandage 109 nii lugejas kui ka nimetajas.

$$\frac{-700\sqrt{109}+32700}{210\sqrt{109}+70850}$$

Ratsionaliseerige korrutades lugeja ja 210\sqrt{109}-70850 nimetaja \frac{-700\sqrt{109}+32700}{210\sqrt{109}+70850} nimetaja.

$$\frac{\left(-700\sqrt{109}+32700\right)\left(210\sqrt{109}-70850\right)}{\left(210\sqrt{109}+70850\right)\left(210\sqrt{109}-70850\right)}$$

Mõelge valemile \left(210\sqrt{109}+70850\right)\left(210\sqrt{109}-70850\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(-700\sqrt{109}+32700\right)\left(210\sqrt{109}-70850\right)}{\left(210\sqrt{109}\right)^{2}-70850^{2}}$$

Laiendage \left(210\sqrt{109}\right)^{2}.

$$\frac{\left(-700\sqrt{109}+32700\right)\left(210\sqrt{109}-70850\right)}{210^{2}\left(\sqrt{109}\right)^{2}-70850^{2}}$$

Arvutage 2 aste 210 ja leidke 44100.

$$\frac{\left(-700\sqrt{109}+32700\right)\left(210\sqrt{109}-70850\right)}{44100\left(\sqrt{109}\right)^{2}-70850^{2}}$$

\sqrt{109} ruut on 109.

$$\frac{\left(-700\sqrt{109}+32700\right)\left(210\sqrt{109}-70850\right)}{44100\times 109-70850^{2}}$$

Korrutage 44100 ja 109, et leida 4806900.

$$\frac{\left(-700\sqrt{109}+32700\right)\left(210\sqrt{109}-70850\right)}{4806900-70850^{2}}$$

Arvutage 2 aste 70850 ja leidke 5019722500.

$$\frac{\left(-700\sqrt{109}+32700\right)\left(210\sqrt{109}-70850\right)}{4806900-5019722500}$$

Lahutage 5019722500 väärtusest 4806900, et leida -5014915600.

$$\frac{\left(-700\sqrt{109}+32700\right)\left(210\sqrt{109}-70850\right)}{-5014915600}$$

Rakendage distributiivsusomadus, korrutades avaldise -700\sqrt{109}+32700 iga liikme avaldise 210\sqrt{109}-70850 iga liikmega.

$$\frac{-147000\left(\sqrt{109}\right)^{2}[phone]\sqrt{109}+6867000\sqrt{109}-2316795000}{-5014915600}$$

\sqrt{109} ruut on 109.

$$\frac{-147000\times 109+49595000\sqrt{109}+6867000\sqrt{109}-2316795000}{-5014915600}$$

Korrutage -147000 ja 109, et leida -16023000.

$$\frac{-16023000+49595000\sqrt{109}+6867000\sqrt{109}-2316795000}{-5014915600}$$

Kombineerige 49595000\sqrt{109} ja 6867000\sqrt{109}, et leida 56462000\sqrt{109}.

$$\frac{-16023000+56462000\sqrt{109}-2316795000}{-5014915600}$$

Lahutage 2316795000 väärtusest -16023000, et leida -2332818000.

$$\frac{-2332818000+56462000\sqrt{109}}{-5014915600}$$

Lahuta teguriteks

$$\frac{5 {(10701 - 259 \sqrt{109})}}{115021} = 0,347630459402725$$