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}|-frac{frac{1}{3}-frac{2}{9}}{frac{1}{8}-frac{15}{8}}=

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

تقييم

$$-\frac{239}{756}\approx -0.316137566$$

خطوات الحل

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

$$\frac{\left(\frac{10}{9}\right)^{2}}{\left(1-\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}+\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$\frac{\frac{100}{81}}{\left(1-\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}+\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$\frac{\frac{100}{81}}{\left(\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}+\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$\frac{\frac{100}{81}}{\frac{1}{4}\left(-2\right)^{3}-\frac{3}{2}}+\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

احسب -2 بالأس 3 لتحصل على -8.

$$\frac{\frac{100}{81}}{\frac{1}{4}\left(-8\right)-\frac{3}{2}}+\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

اضرب \frac{1}{4} في -8 لتحصل على -2.

$$\frac{\frac{100}{81}}{-2-\frac{3}{2}}+\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$\frac{\frac{100}{81}}{-\frac{7}{2}}+\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$\frac{100}{81}\left(-\frac{2}{7}\right)+\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{200}{567}+\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{200}{567}+\frac{1}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

اجمع -\frac{200}{567} مع \frac{1}{36} لتحصل على -\frac{737}{2268}.

$$-\frac{737}{2268}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{737}{2268}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{737}{2268}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{737}{2268}+\frac{\frac{1}{20}}{\frac{9}{25}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{737}{2268}+\frac{1}{20}\times \frac{25}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{737}{2268}+\frac{5}{36}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

اطرح \frac{2}{9} من \frac{1}{3} لتحصل على \frac{1}{9}.

$$-\frac{737}{2268}+\frac{5}{36}|-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

اطرح \frac{15}{8} من \frac{1}{8} لتحصل على -\frac{7}{4}.

$$-\frac{737}{2268}+\frac{5}{36}|-\frac{\frac{1}{9}}{-\frac{7}{4}}|$$

اقسم \frac{1}{9} على -\frac{7}{4} من خلال ضرب \frac{1}{9} في مقلوب -\frac{7}{4}.

$$-\frac{737}{2268}+\frac{5}{36}|-\frac{1}{9}\left(-\frac{4}{7}\right)|$$

اضرب \frac{1}{9} في -\frac{4}{7} لتحصل على -\frac{4}{63}.

$$-\frac{737}{2268}+\frac{5}{36}|-\left(-\frac{4}{63}\right)|$$

مقابل -\frac{4}{63} هو \frac{4}{63}.

$$-\frac{737}{2268}+\frac{5}{36}|\frac{4}{63}|$$

القيمة المطلقة لعدد حقيقي a هي a عندما يكون a\geq 0 أو -a عندما يكون a<0. القيمة المطلقة لـ \frac{4}{63} هي \frac{4}{63}.

$$-\frac{737}{2268}+\frac{5}{36}\times \frac{4}{63}$$

اضرب \frac{5}{36} في \frac{4}{63} لتحصل على \frac{5}{567}.

$$-\frac{737}{2268}+\frac{5}{567}$$

اجمع -\frac{737}{2268} مع \frac{5}{567} لتحصل على -\frac{239}{756}.

$$-\frac{239}{756}$$

تحليل العوامل

$$-\frac{239}{756} = -0.31613756613756616$$