Lahenda sqrt{(40+1/2)(2-1)}-(2/3-1)^-2:(1/5)^-1/(1-frac{1{4})^2}+frac{(frac{2-frac{1}{3}}{frac{3}{2}-1})^-2}{frac{frac{1}{2}-frac{2}{3}}{4-frac{2}{3}}}

$$\sqrt { ( 40 + \frac { 1 } { 2 } ) ( 2 - 1 ) } - \frac { ( \frac { 2 } { 3 } - 1 ) ^ { - 2 } : ( \frac { 1 } { 5 } ) ^ { - 1 } } { ( 1 - \frac { 1 } { 4 } ) ^ { 2 } } + \frac { ( \frac { 2 - \frac { 1 } { 3 } } { \frac { 3 } { 2 } - 1 } ) ^ { - 2 } } { \frac { \frac { 1 } { 2 } - \frac { 2 } { 3 } } { 4 - \frac { 2 } { 3 } } }$$

Arvuta

$$\frac{9\sqrt{2}}{2}-5\approx 1,363961031$$

Lühike lahenduskäik

Liitke 40 ja \frac{1}{2}, et leida \frac{81}{2}.

$$\sqrt{\frac{81}{2}\left(2-1\right)}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Lahutage 1 väärtusest 2, et leida 1.

$$\sqrt{\frac{81}{2}\times 1}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Korrutage \frac{81}{2} ja 1, et leida \frac{81}{2}.

$$\sqrt{\frac{81}{2}}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Kirjutage: allüksus \sqrt{\frac{81}{2}}: allüksus juured \frac{\sqrt{81}}{\sqrt{2}}.

$$\frac{\sqrt{81}}{\sqrt{2}}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Arvutage 81 ruutjuur, et saada 9.

$$\frac{9}{\sqrt{2}}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Ratsionaliseerige korrutades lugeja ja \sqrt{2} nimetaja \frac{9}{\sqrt{2}} nimetaja.

$$\frac{9\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

\sqrt{2} ruut on 2.

$$\frac{9\sqrt{2}}{2}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Lahutage 1 väärtusest \frac{2}{3}, et leida -\frac{1}{3}.

$$\frac{9\sqrt{2}}{2}-\frac{\frac{\left(-\frac{1}{3}\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Arvutage -2 aste -\frac{1}{3} ja leidke 9.

$$\frac{9\sqrt{2}}{2}-\frac{\frac{9}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Arvutage -1 aste \frac{1}{5} ja leidke 5.

$$\frac{9\sqrt{2}}{2}-\frac{\frac{9}{5}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Lahutage \frac{1}{4} väärtusest 1, et leida \frac{3}{4}.

$$\frac{9\sqrt{2}}{2}-\frac{\frac{9}{5}}{\left(\frac{3}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Arvutage 2 aste \frac{3}{4} ja leidke \frac{9}{16}.

$$\frac{9\sqrt{2}}{2}-\frac{\frac{9}{5}}{\frac{9}{16}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Jagage \frac{9}{5} väärtusega \frac{9}{16}, korrutades \frac{9}{5} väärtuse \frac{9}{16} pöördväärtusega.

$$\frac{9\sqrt{2}}{2}-\frac{9}{5}\times \frac{16}{9}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Korrutage \frac{9}{5} ja \frac{16}{9}, et leida \frac{16}{5}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Lahutage \frac{1}{3} väärtusest 2, et leida \frac{5}{3}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\left(\frac{\frac{5}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Lahutage 1 väärtusest \frac{3}{2}, et leida \frac{1}{2}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\left(\frac{\frac{5}{3}}{\frac{1}{2}}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Jagage \frac{5}{3} väärtusega \frac{1}{2}, korrutades \frac{5}{3} väärtuse \frac{1}{2} pöördväärtusega.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\left(\frac{5}{3}\times 2\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Korrutage \frac{5}{3} ja 2, et leida \frac{10}{3}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\left(\frac{10}{3}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Arvutage -2 aste \frac{10}{3} ja leidke \frac{9}{100}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\frac{9}{100}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Lahutage \frac{2}{3} väärtusest \frac{1}{2}, et leida -\frac{1}{6}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\frac{9}{100}}{\frac{-\frac{1}{6}}{4-\frac{2}{3}}}$$

Lahutage \frac{2}{3} väärtusest 4, et leida \frac{10}{3}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\frac{9}{100}}{\frac{-\frac{1}{6}}{\frac{10}{3}}}$$

Jagage -\frac{1}{6} väärtusega \frac{10}{3}, korrutades -\frac{1}{6} väärtuse \frac{10}{3} pöördväärtusega.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\frac{9}{100}}{-\frac{1}{6}\times \frac{3}{10}}$$

Korrutage -\frac{1}{6} ja \frac{3}{10}, et leida -\frac{1}{20}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\frac{9}{100}}{-\frac{1}{20}}$$

Jagage \frac{9}{100} väärtusega -\frac{1}{20}, korrutades \frac{9}{100} väärtuse -\frac{1}{20} pöördväärtusega.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{9}{100}\left(-20\right)$$

Korrutage \frac{9}{100} ja -20, et leida -\frac{9}{5}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}-\frac{9}{5}$$

Lahutage \frac{9}{5} väärtusest -\frac{16}{5}, et leida -5.

$$\frac{9\sqrt{2}}{2}-5$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 5 ja \frac{2}{2}.

$$\frac{9\sqrt{2}}{2}-\frac{5\times 2}{2}$$

Kuna murdudel \frac{9\sqrt{2}}{2} ja \frac{5\times 2}{2} on sama nimetaja, lahutage nende lugejad.

$$\frac{9\sqrt{2}-5\times 2}{2}$$

Tehke korrutustehted võrrandis 9\sqrt{2}-5\times 2.

$$\frac{9\sqrt{2}-10}{2}$$

Lahuta teguriteks

$$\frac{9 \sqrt{2} - 10}{2} = 1,3639610306789285$$