Réitigh -(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}}=

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

Luacháil

$$\frac{3}{7}\approx 0.428571429$$

Céimeanna Réitigh

Suimigh \frac{1}{3} agus \frac{7}{9} chun \frac{10}{9} a fháil.

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

Ríomh cumhacht \frac{10}{9} de 2 agus faigh \frac{100}{81}.

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

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

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

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

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

Ríomh cumhacht -2 de 3 agus faigh -8.

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

Méadaigh \frac{1}{4} agus -8 chun -2 a fháil.

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

Dealaigh \frac{3}{2} ó -2 chun -\frac{7}{2} a fháil.

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

Roinn \frac{100}{81} faoi -\frac{7}{2} trí \frac{100}{81} a mhéadú faoi dheilín -\frac{7}{2}.

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

Méadaigh \frac{100}{81} agus -\frac{2}{7} chun -\frac{200}{567} a fháil.

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

Tá \frac{200}{567} urchomhairleach le -\frac{200}{567}.

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

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

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

Dealaigh \frac{1}{5} ó \frac{1}{4} chun \frac{1}{20} a fháil.

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Dealaigh \frac{2}{5} ó 1 chun \frac{3}{5} a fháil.

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Ríomh cumhacht \frac{3}{5} de 2 agus faigh \frac{9}{25}.

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{\frac{1}{20}}{\frac{9}{25}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Roinn \frac{1}{20} faoi \frac{9}{25} trí \frac{1}{20} a mhéadú faoi dheilín \frac{9}{25}.

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{1}{20}\times \frac{25}{9}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Méadaigh \frac{1}{20} agus \frac{25}{9} chun \frac{5}{36} a fháil.

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

Suimigh -\frac{1}{36} agus \frac{5}{36} chun \frac{1}{9} a fháil.

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

Ríomh cumhacht \frac{1}{9} de 2 agus faigh \frac{1}{81}.

$$\frac{200}{567}+\frac{1}{81}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Suimigh \frac{200}{567} agus \frac{1}{81} chun \frac{23}{63} a fháil.

$$\frac{23}{63}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Dealaigh \frac{2}{9} ó \frac{1}{3} chun \frac{1}{9} a fháil.

$$\frac{23}{63}-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Dealaigh \frac{15}{8} ó \frac{1}{8} chun -\frac{7}{4} a fháil.

$$\frac{23}{63}-\frac{\frac{1}{9}}{-\frac{7}{4}}$$

Roinn \frac{1}{9} faoi -\frac{7}{4} trí \frac{1}{9} a mhéadú faoi dheilín -\frac{7}{4}.

$$\frac{23}{63}-\frac{1}{9}\left(-\frac{4}{7}\right)$$

Méadaigh \frac{1}{9} agus -\frac{4}{7} chun -\frac{4}{63} a fháil.

$$\frac{23}{63}-\left(-\frac{4}{63}\right)$$

Tá \frac{4}{63} urchomhairleach le -\frac{4}{63}.

$$\frac{23}{63}+\frac{4}{63}$$

Suimigh \frac{23}{63} agus \frac{4}{63} chun \frac{3}{7} a fháil.

$$\frac{3}{7}$$

Fachtóirigh

$$\frac{3}{7} = 0.42857142857142855$$