Không quy đồng mẫu, hãy tính hợp lí tổng: A = 1/2.15 + 3/11.2 + 4/1.11 + 5/2.1

Ta có:

\[A = \frac{1}{{2.15}} + \frac{3}{{11.2}} + \frac{4}{{1.11}} + \frac{5}{{2.1}}\]

Suy ra \[\frac{1}{7}A = \frac{1}{{7.2.15}} + \frac{3}{{7.11.2}} + \frac{4}{{7.1.11}} + \frac{5}{{7.2.1}}\]

\[{\rm{ =  }}\frac{1}{{14.15}} + \frac{3}{{11.14}} + \frac{4}{{7.11}} + \frac{5}{{2.7}}\]

\[{\rm{ =  }}\frac{5}{{2.7}} + \frac{4}{{7.11}} + \frac{3}{{11.14}} + \frac{1}{{14.15}}\]

\[{\rm{  =  }}\frac{1}{2} - \frac{1}{7} + \frac{1}{7} - \frac{1}{{11}} + \frac{1}{{11}} - \frac{1}{{14}} + \frac{1}{{14}} - \frac{1}{{15}}\]

\[{\rm{  =  }}\frac{1}{2} - \frac{1}{{15}}\]

\[{\rm{  =  }}\frac{{13}}{{30}}\]

Do đó \[{\rm{A}} = \frac{{13}}{{30}}:\frac{1}{7} = \frac{{13}}{{30}}.7 = \frac{{91}}{{30}}\].