Question

пожалуйста помогите ​

Answer 1

Ответ:

$\frac{5}{69}$

Пошаговое объяснение:

$=\frac{1}{11*15}+\frac{1}{15*19} +\frac{1}{7*11}+\frac{1}{3*7} +\frac{1}{19*23}=\\\\=\frac{11+19}{11*15*19} +\frac{3+11}{3*7*11} +\frac{1}{19*23}=\\\\ =\frac{30}{11*15*19} +\frac{14}{3*7*11} +\frac{1}{19*23}=\\\\ =\frac{2}{11*19} +\frac{2}{3*11} +\frac{1}{19*23}= \\\\=\frac{2(3+19)}{3*11*19} +\frac{1}{19*23}=\frac{2*22}{3*11*19} +\frac{1}{19*23}=\\\\=\frac{2*2}{3*19} +\frac{1}{19*23}=\frac{4*23+3}{3*19*23}=\frac{95}{3*19*23} =\frac{5}{3*23}=\frac{5}{69}$