Réitigh {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}}

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

Luacháil

$$-\frac{704}{1875}\approx -0.375466667$$

Céimeanna Réitigh

Roinn \frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} faoi \frac{5}{6} trí \frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} a mhéadú faoi dheilín \frac{5}{6}.

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

Dealaigh \frac{2}{3} ó \frac{1}{2} chun -\frac{1}{6} a fháil.

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

Ríomh cumhacht -\frac{1}{6} de 2 agus faigh \frac{1}{36}.

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

Méadaigh \frac{1}{36} agus 6 chun \frac{1}{6} a fháil.

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

Méadaigh \frac{5}{6} agus 5 chun \frac{25}{6} a fháil.

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

Roinn \frac{1}{6} faoi \frac{25}{6} trí \frac{1}{6} a mhéadú faoi dheilín \frac{25}{6}.

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

Méadaigh \frac{1}{6} agus \frac{6}{25} chun \frac{1}{25} a fháil.

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

Athscríobh fréamh cearnach na roinnte \frac{1}{9} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{1}}{\sqrt{9}}. Tóg fréamh chearnach an uimhreora agus an ainmneora.

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

Dealaigh \frac{1}{3} ó \frac{1}{25} chun -\frac{22}{75} a fháil.

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

Áirigh \sqrt[3]{\frac{1}{8}} agus faigh \frac{1}{2}.

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

Dealaigh \frac{1}{2} ó 1 chun \frac{1}{2} a fháil.

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

Ríomh cumhacht \frac{1}{2} de 2 agus faigh \frac{1}{4}.

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

Méadaigh \frac{1}{4} agus \frac{9}{8} chun \frac{9}{32} a fháil.

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

Suimigh \frac{1}{2} agus \frac{9}{32} chun \frac{25}{32} a fháil.

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

Roinn -\frac{22}{75} faoi \frac{25}{32} trí -\frac{22}{75} a mhéadú faoi dheilín \frac{25}{32}.

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

Méadaigh -\frac{22}{75} agus \frac{32}{25} chun -\frac{704}{1875} a fháil.

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

Fachtóirigh

$$-\frac{704}{1875} = -0.37546666666666667$$