\(\boxed{\text{51.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\)
Пояснение.
Решение.
\[\textbf{а)}\frac{x}{a - b} = \frac{x \cdot (a - b)}{(a - b) \cdot (a - b)} =\]
\[= \frac{xa - xb}{(a - {b)}^{2}}\]
\[\textbf{б)}\ \frac{y}{x - a} = \frac{y \cdot (x + a)}{(x - a) \cdot (x + a)} =\]
\[= \frac{yx + ya}{x^{2} - a^{2}}\]
\[\textbf{в)}\ \frac{a}{a - 10} = \frac{a \cdot ( - 1)}{(a - 10) \cdot ( - 1)} =\]
\[= \frac{- a}{10 - a} = - \frac{a}{10 - a}\]
\[\textbf{г)}\ \frac{p}{p - 2} =\]
\[= \frac{p \cdot \left( - (p + 2) \right)}{(p - 2) \cdot \left( - (p + 2) \right)} =\]
\[= \frac{- p \cdot (p + 2)}{4 - p^{2}} = - \frac{p^{2} + 2p}{4 - p^{2}}\]
\[\textbf{д)}\ \frac{\text{mn}}{n - m} = - \frac{\text{mn}(m + n)}{(m - n)(m + n)} =\]
\[= - \frac{mn(m + n)}{m^{2} - n^{2}}\]