{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}} eching

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

Baholash

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

Yechim qadamlari

\frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} ni \frac{5}{6} ga bo'lish \frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} ga k'paytirish \frac{5}{6} ga qaytarish.

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

-\frac{1}{6} olish uchun \frac{1}{2} dan \frac{2}{3} ni ayirish.

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

2 daraja ko‘rsatkichini -\frac{1}{6} ga hisoblang va \frac{1}{36} ni qiymatni oling.

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

\frac{1}{6} hosil qilish uchun \frac{1}{36} va 6 ni ko'paytirish.

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

\frac{25}{6} hosil qilish uchun \frac{5}{6} va 5 ni ko'paytirish.

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

\frac{1}{6} ni \frac{25}{6} ga bo'lish \frac{1}{6} ga k'paytirish \frac{25}{6} ga qaytarish.

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

\frac{1}{25} hosil qilish uchun \frac{1}{6} va \frac{6}{25} ni ko'paytirish.

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

\frac{1}{9} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{9}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing. Surat va maxrajni kvadrat ildizdan chiqaring.

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

-\frac{22}{75} olish uchun \frac{1}{25} dan \frac{1}{3} ni ayirish.

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

\sqrt[3]{\frac{1}{8}} ni hisoblab, \frac{1}{2} natijasiga ega bo‘ling.

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

\frac{1}{2} olish uchun 1 dan \frac{1}{2} ni ayirish.

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

2 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va \frac{1}{4} ni qiymatni oling.

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

\frac{9}{32} hosil qilish uchun \frac{1}{4} va \frac{9}{8} ni ko'paytirish.

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

\frac{25}{32} olish uchun \frac{1}{2} va \frac{9}{32}'ni qo'shing.

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

-\frac{22}{75} ni \frac{25}{32} ga bo'lish -\frac{22}{75} ga k'paytirish \frac{25}{32} ga qaytarish.

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

-\frac{704}{1875} hosil qilish uchun -\frac{22}{75} va \frac{32}{25} ni ko'paytirish.

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

Omil

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