2. Упростите: a) (x - 10/y) * (1/(y-x)) б) x^{-10} / (x^4 * x^{-5})

Решение:

а)

\( \left(x - \frac{10}{y} \right) \cdot \frac{1}{y-x} = \left( \frac{xy - 10}{y} \right) \cdot \frac{1}{y-x} = \frac{xy - 10}{y(y-x)} \)

б)

\( \frac{x^{-10}}{x^4 \cdot x^{-5}} = \frac{x^{-10}}{x^{4+(-5)}} = \frac{x^{-10}}{x^{-1}} = x^{-10 - (-1)} = x^{-10+1} = x^{-9} = \frac{1}{x^9} \)

Ответ: а) \( \frac{xy - 10}{y(y-x)} \), б) \( \frac{1}{x^9} \).