[tex]\frac{5}{3*8} +\frac{7}{8*15} + \frac{9}{15*24} + \frac{11}{24*35} =[/tex]
[tex]= \frac{ 8-3}{3*8} +\frac{15-8}{8*15} + \frac{24-15}{15*24} +\frac{35-24}{11*35} =[/tex]
[tex]= \frac{8}{3*8} - \frac{3}{3*8} + \frac{15}{8*15} - \frac{8}{8*15} +\frac{24}{15*24} -\\\\ \frac{15}{15*24} + \frac{35}{24*35} - \frac{24}{24*35} =[/tex]
simplificam fractiile
[tex]= \frac{1}{3} - \frac{1}{8} + \frac{1}{8} - \frac{1}{15} + \frac{1}{15} - \frac{1}{24} + \frac{1}{24} - \frac{1}{35} =[/tex]
reducem fractiile
[tex]= \frac{1}{3} - \frac{1}{35} =[/tex]
amplificam pt numitor comun
[tex]=\frac{35- 2}{3*35} = \frac{32}{105}[/tex]
