номер 109 гдз 8 класс алгебра Муравин Муравин

1)\begin{equation}\frac{c_{100}^{98}+c_{1000}^{998}}{c_{1000}^{2}+c_{100}^{2}} \end{equation} \begin{equation}c_{100}^{98}=c_{100}^{2} \end{equation} \begin{equation}c_{1000}^{998}=c_{1000}^{2} \end{equation} \begin{equation}\frac{c_{100}^{2}+c_{1000}^{2}}{c_{1000}^{2}+c_{100}^{2}}=1 \end{equation} 2)\begin{equation}\frac{n!}{\left ( n-3 \right )!A_{n}^{2}}-\frac{P_{n+1}}{\left ( n+2 \right )!} \end{equation} \begin{equation}\frac{n!}{\left ( n-3 \right )!A_{n}^{2}}=\frac{1-\left ( n-3 \right )\left ( n-2 \right )\left ( n-1 \right )\cdot n}{\left ( n-3 \right )!\cdot \frac{n}{n-2}}= \end{equation} \begin{equation}=\left ( n-2 \right )^{2}\left ( n-1 \right ) \end{equation} \begin{equation}\frac{P_{n+1}}{\left ( n+2 \right )!}=\frac{n\left ( n+1 \right )}{n\cdot \left ( n+1 \right )\left ( n+2 \right )}=\frac{1}{n+2} \end{equation} \begin{equation}\left ( n-2 \right )^{2}\left ( n-1 \right )-\frac{1}{n+2}=\frac{n^{2}-5}{n+2} \end{equation} 3)\begin{equation}\left ( \frac{1}{n!}+\frac{1}{\left ( n+1 \right )!} \right )\cdot n! \end{equation} \begin{equation}\frac{n!}{n!}+\frac{n!}{\left ( n+1 \right )!}=1+\frac{n!}{n!\left ( n+1 \right )}= \end{equation} \begin{equation}=1+\frac{1}{n+1}=\frac{n+1+1}{n+1}= \end{equation} \begin{equation}=\frac{n+2}{n+1} \end{equation} 4)\begin{equation}\left ( \frac{1}{m!}+\frac{1}{\left ( m+1 \right )!} \right )\left ( m+1 \right )! \end{equation} \begin{equation}\frac{\left ( m+1 \right )!}{m!}+\frac{\left ( m+1 \right )!}{\left ( m+1 \right )!}= \end{equation} \begin{equation}=\frac{m!\left ( m+1 \right )}{m!}+1=m+1+1=m+2 \end{equation}