Lahenda {left(frac{1/2-frac{2/3right)}^2}{5/6}-sqrt{1/9}}{sqrt[3]{frac{1}{8}}+{left(1-frac{1}{2}right)}^2frac{9}{8}}

$$\frac{ \frac{ { \left( \frac{ 1 }{ 2 } - \frac{ 2 }{ 3 } \right) }^{ 2 } }{ \frac{ 5 }{ 6 } } - \sqrt{ \frac{ 1 }{ 9 } } }{ \sqrt[ 3 ]{ \frac{ 1 }{ 8 } } + { \left(1- \frac{ 1 }{ 2 } \right) }^{ 2 } \frac{ 9 }{ 8 } }$$

Arvuta

$$-\frac{48}{125}=-0,384$$

Lahenduse etapid

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

$$\frac{\frac{\left(-\frac{1}{6}\right)^{2}}{\frac{5}{6}}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Arvutage 2 aste -\frac{1}{6} ja leidke \frac{1}{36}.

$$\frac{\frac{\frac{1}{36}}{\frac{5}{6}}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Jagage \frac{1}{36} väärtusega \frac{5}{6}, korrutades \frac{1}{36} väärtuse \frac{5}{6} pöördväärtusega.

$$\frac{\frac{1}{36}\times \frac{6}{5}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Korrutage \frac{1}{36} ja \frac{6}{5}, et leida \frac{1}{30}.

$$\frac{\frac{1}{30}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Kirjutage: allüksus \frac{1}{9}: allüksus juured \frac{\sqrt{1}}{\sqrt{9}}. Arvutage nii nimetaja kui ka lugeja ruutjuur.

$$\frac{\frac{1}{30}-\frac{1}{3}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Lahutage \frac{1}{3} väärtusest \frac{1}{30}, et leida -\frac{3}{10}.

$$\frac{-\frac{3}{10}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Arvutage \sqrt[3]{\frac{1}{8}}, et saada \frac{1}{2}.

$$\frac{-\frac{3}{10}}{\frac{1}{2}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

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

$$\frac{-\frac{3}{10}}{\frac{1}{2}+\left(\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Arvutage 2 aste \frac{1}{2} ja leidke \frac{1}{4}.

$$\frac{-\frac{3}{10}}{\frac{1}{2}+\frac{1}{4}\times \frac{9}{8}}$$

Korrutage \frac{1}{4} ja \frac{9}{8}, et leida \frac{9}{32}.

$$\frac{-\frac{3}{10}}{\frac{1}{2}+\frac{9}{32}}$$

Liitke \frac{1}{2} ja \frac{9}{32}, et leida \frac{25}{32}.

$$\frac{-\frac{3}{10}}{\frac{25}{32}}$$

Jagage -\frac{3}{10} väärtusega \frac{25}{32}, korrutades -\frac{3}{10} väärtuse \frac{25}{32} pöördväärtusega.

$$-\frac{3}{10}\times \frac{32}{25}$$

Korrutage -\frac{3}{10} ja \frac{32}{25}, et leida -\frac{48}{125}.

$$-\frac{48}{125}$$

Lahuta teguriteks

$$-\frac{48}{125} = -0,384$$