5. Представьте дробь 42/90 в виде суммы трех дробей, у каждой из которых числитель равен 1.

Сократим дробь:

$\backslash (\backslash frac\{42\}\{90\}\backslash )=\backslash (\backslash frac\{7\}\{15\}\backslash )$.

Подберём три дроби с числителем 1:

$\backslash (\backslash frac\{7\}\{15\}\backslash )=\backslash (\backslash frac\{1\}\{3\}\backslash )+\backslash (\backslash frac\{1\}\{8\}\backslash )+\backslash (\backslash frac\{1\}\{120\}\backslash )$, потому что $\backslash (\backslash frac\{1\}\{3\}\backslash )+\backslash (\backslash frac\{1\}\{8\}\backslash )+\backslash (\backslash frac\{1\}\{120\}\backslash )=\backslash (\backslash frac\{40\}\{120\}\backslash )+\backslash (\backslash frac\{15\}\{120\}\backslash )+\backslash (\backslash frac\{1\}\{120\}\backslash )=\backslash (\backslash frac\{56\}\{120\}\backslash )=\backslash (\backslash frac\{7\}\{15\}\backslash )$.

Ответ: $\backslash (\backslash frac\{42\}\{90\}\backslash )=\backslash (\backslash frac\{1\}\{3\}\backslash )+\backslash (\backslash frac\{1\}\{8\}\backslash )+\backslash (\backslash frac\{1\}\{120\}\backslash )$.