Сократите дробь: (5a-a^2)/(5+34a-7a^2).

Ответ:

\[\frac{5a - a^{2}}{5 + 34a - 7a^{2}} =\]

\[= \frac{- a(a - 5)}{- \left( 7a^{2} - 34a - 5 \right)} =\]

\[= \frac{a(a - 5)}{7 \cdot (a - 5)\left( a + \frac{1}{7} \right)} = \frac{a}{7a + 1}\ \]

\[7a^{2} - 34a - 5 = 0\]

\[D = 289 + 35 = 324\]

\[a_{1} = \frac{17 + 18}{7} = \frac{35}{7} = 5;\ \ \ \ \]

\[a_{2} = \frac{17 - 18}{7} = - \frac{1}{7}\]