Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 1097

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\[1)\ \frac{7! - 5!}{5!} = \frac{7 \bullet 6 \bullet 5! - 5!}{5!} =\]

\[= 7 \bullet 6 - 1 = 42 - 1 = 41;\]

\[2)\ \frac{6! - 4!}{5!} = \frac{6 \bullet 5 \bullet 4! - 4!}{5 \bullet 4!} =\]

\[= \frac{6 \bullet 5 - 1}{5} = \frac{30 - 1}{5} = \frac{29}{5} = 5,8;\]

\[3)\ \frac{149!}{148!} - \frac{36!}{35!} =\]

\[= \frac{149 \bullet 148!}{148!} - \frac{36 \bullet 35!}{35!} =\]

\[= 149 - 36 = 113;\]

\[4)\ \frac{97!}{96!} + \frac{35!}{34!} =\]

\[= \frac{97 \bullet 96!}{96!} + \frac{35 \bullet 34!}{34!} = 97 + 35 =\]

\[= 132;\]

\[5)\ \frac{4! \bullet 8!}{6! \bullet 7!} = \frac{4! \bullet 8 \bullet 7!}{6 \bullet 5 \bullet 4! \bullet 7!} = \frac{8}{6 \bullet 5} =\]

\[= \frac{8}{30} = \frac{4}{15};\]

\[6)\ \frac{9! \bullet 5!}{7! \bullet 6!} = \frac{9 \bullet 8 \bullet 7! \bullet 5!}{7! \bullet 6 \bullet 5!} = \frac{9 \bullet 8}{6} =\]

\[= \frac{72}{6} = 12.\]