Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 185

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\[1)\ y = \frac{10 - 3x}{x - 4}\text{\ \ }и\ \ y = \frac{4x + 10}{x + 3}\]

\[y = \frac{10 - 3x}{x - 4}\]

\[x = \frac{10 - 3y}{y - 4}\]

\[x(y - 4) = 10 - 3y\]

\[xy - 4x = 10 - 3y\]

\[xy + 3y = 10 + 4x\]

\[y(x + 3) = 4x + 10\]

\[y = \frac{4x + 10}{x + 3}\]

\[Ответ:\ \ являются.\]

\[2)\ y = \frac{3x - 6}{3x - 1}\text{\ \ }и\ \ y = \frac{6 - x}{3 - 3x}\]

\[y = \frac{3x - 6}{3x - 1}\]

\[x = \frac{3y - 6}{3y - 1}\]

\[x(3y - 1) = 3y - 6\]

\[3xy - x = 3y - 6\]

\[3xy - 3y = x - 6\]

\[y(3x - 3) = x - 6\]

\[y = \frac{x - 6}{3x - 3}\]

\[y = \frac{6 - x}{3 - 3x}\]

\[Ответ:\ \ являются.\]

\[3)\ y = 5(1 - x)^{- 1}\text{\ \ }и\ \ \]

\[y = (5 - x) \bullet x^{- 1};\]

\[y = 5(1 - x)^{- 1}\]

\[x = 5(1 - y)^{- 1}\]

\[x = \frac{5}{1 - y}\]

\[x(1 - y) = 5\]

\[x - xy = 5\]

\[xy = x - 5\]

\[y = \frac{x - 5}{x}\]

\[y = (x - 5) \bullet x^{- 1}\]

\[Ответ:\ \ не\ являются.\]

\[4)\ y = \frac{2 - x}{2 + x}\text{\ \ }и\ \ y = \frac{2(x - 1)}{1 + x}\]

\[y = \frac{2 - x}{2 + x}\text{\ \ }\]

\[x = \frac{2 - y}{2 + y}\]

\[x(2 + y) = 2 - y\]

\[2x + xy = 2 - y\]

\[xy + y = 2 - 2x\]

\[y(x + 1) = 2(1 - x)\]

\[y = \frac{2(1 - x)}{1 + x}\]

\[Ответ:\ \ не\ являются\text{.\ }\]