Resolver (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}}=

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

Ebaluatu

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

Ebazpidea

\frac{10}{9} lortzeko, gehitu \frac{1}{3} eta \frac{7}{9}.

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

\frac{100}{81} lortzeko, egin \frac{10}{9} ber 2.

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

\frac{1}{2} lortzeko, 1 balioari kendu \frac{1}{2}.

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

\frac{1}{4} lortzeko, egin \frac{1}{2} ber 2.

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

-8 lortzeko, egin -2 ber 3.

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

-2 lortzeko, biderkatu \frac{1}{4} eta -8.

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

-\frac{7}{2} lortzeko, -2 balioari kendu \frac{3}{2}.

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

Zatitu \frac{100}{81} balioa -\frac{7}{2} frakzioarekin, \frac{100}{81} balioa -\frac{7}{2} frakzioaren frakzio erreziprokoarekin biderkatuz.

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

-\frac{200}{567} lortzeko, biderkatu \frac{100}{81} eta -\frac{2}{7}.

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

\frac{1}{36} lortzeko, egin -\frac{1}{6} ber 2.

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

-\frac{737}{2268} lortzeko, gehitu -\frac{200}{567} eta \frac{1}{36}.

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

\frac{1}{20} lortzeko, \frac{1}{4} balioari kendu \frac{1}{5}.

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

\frac{3}{5} lortzeko, 1 balioari kendu \frac{2}{5}.

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

\frac{9}{25} lortzeko, egin \frac{3}{5} ber 2.

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

Zatitu \frac{1}{20} balioa \frac{9}{25} frakzioarekin, \frac{1}{20} balioa \frac{9}{25} frakzioaren frakzio erreziprokoarekin biderkatuz.

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

\frac{5}{36} lortzeko, biderkatu \frac{1}{20} eta \frac{25}{9}.

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

\frac{1}{9} lortzeko, \frac{1}{3} balioari kendu \frac{2}{9}.

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

-\frac{7}{4} lortzeko, \frac{1}{8} balioari kendu \frac{15}{8}.

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

Zatitu \frac{1}{9} balioa -\frac{7}{4} frakzioarekin, \frac{1}{9} balioa -\frac{7}{4} frakzioaren frakzio erreziprokoarekin biderkatuz.

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

-\frac{4}{63} lortzeko, biderkatu \frac{1}{9} eta -\frac{4}{7}.

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

-\frac{4}{63} zenbakiaren aurkakoa \frac{4}{63} da.

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

a zenbaki erreal baten balio absolutua a da baldin eta a\geq 0 bada, edo -a a<0 bada. \frac{4}{63} balioaren balio absolutua \frac{4}{63} da.

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

\frac{5}{567} lortzeko, biderkatu \frac{5}{36} eta \frac{4}{63}.

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

-\frac{239}{756} lortzeko, gehitu -\frac{737}{2268} eta \frac{5}{567}.

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

Faktorizatu

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