Resolver (1-1/2)^2(-2)^3-3/2+-(-1/6)^2+frac{1/4-frac{1}{5}}{(1-frac{2}{5})^2}|-frac{frac{1}{3}-frac{2}{9}}{frac{1}{8}-frac{15}{8}}

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

Ebaluatu

$$-\frac{7981}{2268}\approx -3.518959436$$

Ebazpidea

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

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

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

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

-8 lortzeko, egin -2 ber 3.

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

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

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

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

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

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

$$-\frac{7}{2}-\frac{1}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

-\frac{127}{36} lortzeko, -\frac{7}{2} balioari kendu \frac{1}{36}.

$$-\frac{127}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{127}{36}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{127}{36}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{127}{36}+\frac{\frac{1}{20}}{\frac{9}{25}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{127}{36}+\frac{1}{20}\times \frac{25}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{127}{36}+\frac{5}{36}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{127}{36}+\frac{5}{36}|-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

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

$$-\frac{127}{36}+\frac{5}{36}|-\frac{\frac{1}{9}}{-\frac{7}{4}}|$$

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

$$-\frac{127}{36}+\frac{5}{36}|-\frac{1}{9}\left(-\frac{4}{7}\right)|$$

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

$$-\frac{127}{36}+\frac{5}{36}|-\left(-\frac{4}{63}\right)|$$

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

$$-\frac{127}{36}+\frac{5}{36}|\frac{4}{63}|$$

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.

$$-\frac{127}{36}+\frac{5}{36}\times \frac{4}{63}$$

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

$$-\frac{127}{36}+\frac{5}{567}$$

-\frac{7981}{2268} lortzeko, gehitu -\frac{127}{36} eta \frac{5}{567}.

$$-\frac{7981}{2268}$$

Faktorizatu

$$-\frac{7981}{2268} = -3\frac{1177}{2268} = -3.5189594356261025$$