Răspuns:
[tex]( \frac{3}{4} \div \frac{5}{6} ) \div ( \frac{2}{9} \div \frac{8}{3})) + \frac{2}{3} \times \frac{9}{4} \div \frac{3}{2} [/tex]
[tex] = ( \frac{3}{4} \times \frac{6}{5} ) \div ( \frac{2}{9} \times \frac{3}{8} )) + \frac{2}{3} \times \frac{9}{4} \div \frac{3}{2} [/tex]
simplificam 6 si 4 din prima paranteza, cu 2
din a doua paranteza simplificam 2 cu 8 prin 2 si 3 cu 9 prin 3. Dupa aceea obtinem:
[tex] = ( \frac{9}{10} \div \frac{1}{6}) + \frac{2}{3} \times \frac{9}{4} \div \frac{3}{2} [/tex]
[tex] \frac{9}{10} \times \frac{6}{1} + \frac{2}{3} \times \frac{9}{4} \times \frac{2}{3} [/tex]
[tex] = \frac{54}{10} + \frac{2}{3} \times \frac{9}{4} \times \frac{2}{3} [/tex]
simplifi am pe 2 cu 4 prin 2 si pe 3 cu 9 prin 3
[tex] = \frac{54}{10} + \frac{3}{2} \times \frac{2}{3} [/tex]
[tex] = \frac{54}{10} + \frac{1}{1} [/tex]
amplificam a doua fractie cu 10 si obtinem
[tex] = \frac{64}{10} [/tex]
simplificam prin 2 si obtinem
[tex] \frac{32}{5} [/tex]
