حل -(1/3+frac{7/9)^{2}}{(1-1/2)^{2}*(-2)^3-3/2}+-(-frac{1}{6})^2+frac{frac{1}{4}-frac{1}{5}}{(1-frac{2}{5})^2})^2-frac{frac{1}{3}-frac{2}{9}}{frac{1}{8}-frac{15}{8}}=

$$- \frac { ( \frac { 1 } { 3 } + \frac { 7 } { 9 } ) ^ { 2 } } { ( 1 - \frac { 1 } { 2 } ) ^ { 2 } \cdot ( - 2 ) ^ { 3 } - \frac { 3 } { 2 } } + - ( - \frac { 1 } { 6 } ) ^ { 2 } + \frac { \frac { 1 } { 4 } - \frac { 1 } { 5 } } { ( 1 - \frac { 2 } { 5 } ) ^ { 2 } } ) ^ { 2 } - \frac { \frac { 1 } { 3 } - \frac { 2 } { 9 } } { \frac { 1 } { 8 } - \frac { 15 } { 8 } } =$$

تقييم

$$\frac{263}{567}\approx 0.463844797$$

خطوات الحل

اجمع \frac{1}{3} مع \frac{7}{9} لتحصل على \frac{10}{9}.

$$-\frac{\left(\frac{10}{9}\right)^{2}}{\left(1-\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

احسب \frac{10}{9} بالأس 2 لتحصل على \frac{100}{81}.

$$-\frac{\frac{100}{81}}{\left(1-\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

اطرح \frac{1}{2} من 1 لتحصل على \frac{1}{2}.

$$-\frac{\frac{100}{81}}{\left(\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

احسب \frac{1}{2} بالأس 2 لتحصل على \frac{1}{4}.

$$-\frac{\frac{100}{81}}{\frac{1}{4}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

احسب -2 بالأس 3 لتحصل على -8.

$$-\frac{\frac{100}{81}}{\frac{1}{4}\left(-8\right)-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

اضرب \frac{1}{4} في -8 لتحصل على -2.

$$-\frac{\frac{100}{81}}{-2-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

اطرح \frac{3}{2} من -2 لتحصل على -\frac{7}{2}.

$$-\frac{\frac{100}{81}}{-\frac{7}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

اقسم \frac{100}{81} على -\frac{7}{2} من خلال ضرب \frac{100}{81} في مقلوب -\frac{7}{2}.

$$-\frac{100}{81}\left(-\frac{2}{7}\right)-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

اضرب \frac{100}{81} في -\frac{2}{7} لتحصل على -\frac{200}{567}.

$$-\left(-\frac{200}{567}\right)-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

مقابل -\frac{200}{567} هو \frac{200}{567}.

$$\frac{200}{567}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

احسب -\frac{1}{6} بالأس 2 لتحصل على \frac{1}{36}.

$$\frac{200}{567}-\frac{1}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

اطرح \frac{1}{36} من \frac{200}{567} لتحصل على \frac{737}{2268}.

$$\frac{737}{2268}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

اطرح \frac{1}{5} من \frac{1}{4} لتحصل على \frac{1}{20}.

$$\frac{737}{2268}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}$$

اطرح \frac{2}{5} من 1 لتحصل على \frac{3}{5}.

$$\frac{737}{2268}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}$$

احسب \frac{3}{5} بالأس 2 لتحصل على \frac{9}{25}.

$$\frac{737}{2268}+\frac{\frac{1}{20}}{\frac{9}{25}}$$

اقسم \frac{1}{20} على \frac{9}{25} من خلال ضرب \frac{1}{20} في مقلوب \frac{9}{25}.

$$\frac{737}{2268}+\frac{1}{20}\times \frac{25}{9}$$

اضرب \frac{1}{20} في \frac{25}{9} لتحصل على \frac{5}{36}.

$$\frac{737}{2268}+\frac{5}{36}$$

اجمع \frac{737}{2268} مع \frac{5}{36} لتحصل على \frac{263}{567}.

$$\frac{263}{567}$$

تحليل العوامل

$$\frac{263}{3 ^ {4} \cdot 7} = 0.4638447971781305$$