Question

Rezolvati: $\frac{(\frac{1}{2} ) ^{-2} -5(-2) ^{-2} + (\frac{2}{3})^{-2}} \frac({3}{/8})^{-1}* (\frac{3}{2})^{3}+ (-\frac{1}{3})^{-1}$

Answer 1

$\displaystyle \frac{\left( \frac{1}{2} \right)^{-2}-5(-2)^{-2}+\left( \frac{2}{3} \right)^{-2}}{\left( \frac{3}{8} \right)^{-1} \cdot \left( \frac{3}{2} \right)^3+\left(- \frac{1}{3} \right)^{-1}} = \frac{2^2-5 \cdot \frac{1}{(-2)^2}+ \frac{3^2}{2^2} }{ \frac{8}{3} \cdot \frac{3^3}{2^3} - 3} = \frac{4-5 \cdot \frac{1}{4} + \frac{9}{4} }{ \frac{8}{3} \cdot \frac{27}{8} -3 } =$

$\displaystyle = \frac{4- \frac{5}{4} + \frac{9}{4} }{ \frac{216}{24} -3} = \frac{ \frac{16-5+9}{4} }{9-3} = \frac{ \frac{20}{4} }6} = \frac{5}{6}$