Реши уравнение: 5/6a-4/5a+1=1/2a-2/5.

Ответ:

\[\frac{5}{6}a - \frac{4}{5}a + 1 = \frac{1}{2}a - \frac{2}{5}\]

\[\frac{5}{6}a - \frac{4}{5}a - \frac{1}{2}a = - \frac{2}{5} - 1^{\backslash 5}\]

\[a\left( \frac{5^{\backslash 10}}{6} - \frac{4^{\backslash 12}}{5} - \frac{1^{\backslash 30}}{2} \right) = \frac{- 2 - 5}{5}\ \]

\[a\left( \frac{50 - 48 - 30}{60} \right) = - \frac{7}{5}\]

\[- \frac{28}{60}a = - \frac{7}{5}\]

\[a = \frac{7}{5} \cdot \frac{60}{28} =\]

\[a = \frac{7 \cdot 5 \cdot 12}{5 \cdot 7 \cdot 4}\]

\[a = 3.\]