Atrisiniet {left(frac{1/2-frac{2/3right)}^2}{5/6}div5/6-sqrt{frac{1}{9}}}{sqrt[3]{frac{1}{8}}+{left(1-frac{1}{2}right)}^2frac{9}{8}}

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

Izrēķināt

$$-\frac{704}{1875}\approx -0,375466667$$

Atrisinājuma darbības

Daliet \frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} ar \frac{5}{6}, reizinot \frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} ar apgriezto daļskaitli \frac{5}{6} .

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

Atņemiet \frac{2}{3} no \frac{1}{2}, lai iegūtu -\frac{1}{6}.

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

Aprēķiniet -\frac{1}{6} pakāpē 2 un iegūstiet \frac{1}{36}.

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

Reiziniet \frac{1}{36} un 6, lai iegūtu \frac{1}{6}.

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

Reiziniet \frac{5}{6} un 5, lai iegūtu \frac{25}{6}.

$$\frac{\frac{\frac{1}{6}}{\frac{25}{6}}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Daliet \frac{1}{6} ar \frac{25}{6}, reizinot \frac{1}{6} ar apgriezto daļskaitli \frac{25}{6} .

$$\frac{\frac{1}{6}\times \frac{6}{25}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Reiziniet \frac{1}{6} un \frac{6}{25}, lai iegūtu \frac{1}{25}.

$$\frac{\frac{1}{25}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Pārrakstiet dalījuma kvadrātsakni \frac{1}{9} kā kvadrātveida saknes \frac{\sqrt{1}}{\sqrt{9}}. Izrēķiniet gan skaitītāja, gan saucēja kvadrātsakni.

$$\frac{\frac{1}{25}-\frac{1}{3}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Atņemiet \frac{1}{3} no \frac{1}{25}, lai iegūtu -\frac{22}{75}.

$$\frac{-\frac{22}{75}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Aprēķināt \sqrt[3]{\frac{1}{8}} un iegūt \frac{1}{2}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Atņemiet \frac{1}{2} no 1, lai iegūtu \frac{1}{2}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\left(\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Aprēķiniet \frac{1}{2} pakāpē 2 un iegūstiet \frac{1}{4}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\frac{1}{4}\times \frac{9}{8}}$$

Reiziniet \frac{1}{4} un \frac{9}{8}, lai iegūtu \frac{9}{32}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\frac{9}{32}}$$

Saskaitiet \frac{1}{2} un \frac{9}{32}, lai iegūtu \frac{25}{32}.

$$\frac{-\frac{22}{75}}{\frac{25}{32}}$$

Daliet -\frac{22}{75} ar \frac{25}{32}, reizinot -\frac{22}{75} ar apgriezto daļskaitli \frac{25}{32} .

$$-\frac{22}{75}\times \frac{32}{25}$$

Reiziniet -\frac{22}{75} un \frac{32}{25}, lai iegūtu -\frac{704}{1875}.

$$-\frac{704}{1875}$$

Sadalīt reizinātājos

$$-\frac{704}{1875} = -0,37546666666666667$$