Răspuns:
a) 1/2
b) 5/7
c) 1/3
d) 37/4
Explicație pas cu pas:
a)
[tex]= [\frac{3}{4} +\frac{2}{3} :(\frac{3}{4} -\frac{2}{4} )]*\frac{6}{41} =(\frac{3}{4} +\frac{2}{3} :\frac{1}{4} )*\frac{6}{41} =[/tex]
[tex]=(\frac{3}{4} +\frac{2}{3}*4 )*\frac{6}{41} =(\frac{3}{4} +\frac{8}{3})*\frac{6}{41}=[/tex]
[tex]=\frac{9+32}{12}*\frac{6}{41}=\frac{41}{12}*\frac{6}{41}=\frac{1}{2}[/tex]
b)
[tex]=[\frac{7}{15} *\frac{15}{14} +\frac{3}{2} :(\frac{9}{4} -\frac{3}{2} )]*\frac{2}{7} =[\frac{1}{2} +\frac{3}{2} :(\frac{9}{4} -\frac{6}{4} )]*\frac{2}{7} =[/tex]
[tex]=(\frac{1}{2} +\frac{3}{2} :\frac{3}{4})*\frac{2}{7} =(\frac{1}{2} +\frac{3}{2} *\frac{4}{3})*\frac{2}{7} =[/tex]
[tex]=(\frac{1}{2} +\frac{4}{2})*\frac{2}{7} =\frac{5}{2} *\frac{2}{7}=\frac{5}{7}[/tex]
c)
[tex]=(\frac{17}{3} +\frac{14}{9} -2):\frac{47}{3} =(\frac{51}{9} +\frac{14}{9} -\frac{18}{9} )*\frac{3}{47} =\frac{47}{9} *\frac{3}{47}=\frac{1}{3}[/tex]
d)
[tex]=[4+\frac{20}{3} -\frac{9}{4} *(\frac{6}{9} -\frac{2}{9} )]:\frac{29}{6} +\frac{29}{4} =(4+\frac{20}{3}-\frac{9}{4} *\frac{4}{9} )*\frac{6}{29} +\frac{29}{4}=[/tex]
[tex]=(4+\frac{20}{3}-1)*\frac{6}{29} +\frac{29}{4}=(3+\frac{20}{3})*\frac{6}{29} +\frac{29}{4}=\frac{29}{3}*\frac{6}{29} +\frac{29}{4}=[/tex]
[tex]=2+\frac{29}{4}=\frac{8+29}{4} =\frac{37}{4}[/tex]
