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номер 121 гдз 8 класс алгебра Муравин Муравин

1)\begin{equation}\frac{x-a}{x-b}, x=\frac{ab}{a+b} \end{equation} \begin{equation}\frac{\frac{ab}{a+b}-a}{\frac{ab}{a+b}-b} \end{equation} 1)\begin{equation}\frac{ab}{a+b}-a=\frac{ab-a^{2}-ab}{a+b}= \end{equation} \begin{equation}=-\frac{a^{2}}{a+b} \end{equation} 2)\begin{equation}\frac{ab}{a+b}-b=\frac{ab-ab-b^{2}}{a+b}= \end{equation} \begin{equation}=-\frac{b^{2}}{a+b} \end{equation} 3)\begin{equation}-\frac{a^{2}}{a+b}:\left ( -\frac{b^{2}}{a+b} \right )= \end{equation} \begin{equation} =\frac{a^{2}}{a+b}\cdot \frac{a+b}{b^{2}}=\frac{a^{2}}{b^{2}} \end{equation} 2)\begin{equation}\frac{a^{2}-abx}{b^{2}+abx}, x=\frac{a-b}{a+b} \end{equation} \begin{equation} \frac{a^{2}-ba\cdot \frac{a-b}{a+b}}{b^{2}+ab\cdot \frac{a-b}{a+b}} \end{equation} 1)\begin{equation}a^{2}-ab\frac{\left ( a-b \right )}{a+b}= \end{equation} \begin{equation}=\frac{a^{3}+a^{2}b-a^{2}b+ab^{2}}{a+b}= \end{equation} \begin{equation}=\frac{a^{3}+ab^{2}}{a+b}=\frac{a\left ( a^{2}+b^{2} \right )}{a+b} \end{equation} 2)\begin{equation}b^{2}+ab\cdot \frac{\left ( a-b \right )}{a+b}= \end{equation} \begin{equation}=\frac{ab^{2}+b^{3}+a^{2}b-ab^{2}}{a+b}= \end{equation} \begin{equation}=\frac{b\left ( b^{2}+a^{2} \right )}{a+b} \end{equation} 3)\begin{equation}\frac{a\left ( a^{2}+b^{2} \right )}{a+b}:\frac{b\left ( b^{2}+a^{2} \right )}{a+b}= \end{equation} \begin{equation}=\frac{a\left ( a^{2}+b^{2} \right )}{a+b}\cdot \frac{a+b}{b\left ( b^{2}+a^{2} \right )}=\frac{a}{b} \end{equation} 3)\begin{equation}\frac{ax}{x-a}-\frac{bx}{x-b}, x=\frac{ab}{a+b} \end{equation} \begin{equation}\frac{a\cdot \frac{ab}{a+b}}{\frac{ab}{a+b}-a}-\frac{b\cdot \frac{ab}{a+b}}{\frac{ab}{a+b}-b} \end{equation} 1)\begin{equation}\frac{a^{2}b}{a+b}:\frac{ab-a^{2}-ab}{a+b}= \end{equation} \begin{equation}=\frac{a^{2}b}{a+b}\cdot -\frac{a+b}{a^{2}}=-b \end{equation} 2)\begin{equation}\frac{ab^{2}}{a+b}:\frac{ab-ab-b^{2}}{a+b}= \end{equation} \begin{equation}=\frac{ab^{2}\left ( a+b \right )}{\left ( a+b \right )\left ( -b^{2} \right )}=-a \end{equation}
3) -b - (-a) = a - b
4)\begin{equation}\frac{bx}{x-a}+\frac{ax}{x-b}, x=\frac{ab}{a+b} \end{equation} \begin{equation}\frac{b\cdot \frac{ab}{a+b}}{\frac{ab}{a+b}-a}+\frac{a\cdot \frac{ab}{a+b}}{\frac{ab}{a+b}-b} \end{equation} 1)\begin{equation}\frac{ab^{2}}{a+b}:\frac{ab-a^{2}-ab}{a+b}= \end{equation} \begin{equation}=\frac{ab^{2}}{a+b}\cdot \frac{a+b}{-a^{2}}=\frac{-b^{2}}{a} \end{equation} 2)\begin{equation}\frac{a^{2}b}{a+b}:\frac{ab-ab-b^{2}}{a+b}= \end{equation} \begin{equation}=\frac{a^{2}b}{a+b}\cdot \frac{a+b}{-b^{2}}=\frac{-a^{2}}{b} \end{equation} 3)\begin{equation}-\frac{b^{2}}{a}+\left ( -\frac{a^{2}}{b} \right )= \end{equation} \begin{equation}=-\frac{b^{2}}{a}-\frac{a^{2}}{b}=\frac{-b^{3}-a^{3}}{ab}= \end{equation} \begin{equation}=-\frac{a^{3}+b^{3}}{ab} \end{equation}