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Номер 51 гдз 8 класс алгебра Муравин Муравина


Номер 51

 

\begin{equation} 1)\frac{x^{2}-cy+cx-y^{2}}{x^{2}+cy-cx-y^{2}}= \end{equation} \begin{equation} =\frac{(x^{2}-y^{2})+c(x-y)}{(x^{2}-y^{2})-c(x-y)}= \end{equation} \begin{equation} =\frac{(x-y)(x+y)+c(x-y)}{(x-y)(x+y)-c(x-y)}= \end{equation} \begin{equation} =\frac{(x-y)(x+y+c)}{(x-y)(x+y-c)}= \end{equation} \begin{equation} =\frac{x+y+c}{x+y-c}; \end{equation} \begin{equation} 2)\frac{a^{2}+bx-b^{2}+ax}{ab+x^{2}+ax-b^{2}} \end{equation} \begin{equation} x^{2}\rightarrow a^{2} \end{equation} \begin{equation} \frac{(a^{2}-b^{2})+(bx+ax)}{(a^{2}-b^{2})+(ab+ax)}= \end{equation} \begin{equation} =\frac{(a-b)(a+b)+x(a+b)}{(a-b)(a+b)+a(b+x)} \end{equation} \begin{equation} \frac{(a^{2}-b^{2})+(bx+ax)}{(ab-b^{2})+(x^{2}+ax)}= \end{equation} \begin{equation} =\frac{(a^{2}-b^{2})+x(b+a)}{b(a-b)+x(x+a)} \end{equation} \begin{equation} \frac{(a^{2}+ax)+(bx-b^{2})}{(ab+ax)+(x^{2}-b^{2})}= \end{equation} \begin{equation} =\frac{a(a+x)+b(x-b)}{a(b+x)-(x-b)(x+b)}; \end{equation} \begin{equation} 3)\frac{x(y+1)^{2}-y(x+1)^{2}}{x^{2}(y+1)-y^{2}(x+1)} \end{equation} \begin{equation} \frac{x(y^{2}+2y+1)-}{x^{2}y+x^{2}-} \end{equation} \begin{equation} \frac{-y(x^{2}+2x+1}{-y^{2}x-y^{2}}= \end{equation} \begin{equation} =\frac{xy^{2}+2xy+x-}{x^{2}y+x^{2}-} \end{equation} \begin{equation} \frac{x^{2}y-2xy-y}{-y^{2}x-y^{2}}= \end{equation} \begin{equation} =\frac{xy^{2}+x-x^{2}y-y}{x^{2}y+x^{2}-y^{2}x-y^{2}}= \end{equation} \begin{equation} =\frac{(xy^{2}-x^{2}y)+(x-y)}{(x^{2}y-y^{2}x)+(x^{2}-y^{2})}= \end{equation} \begin{equation} =\frac{xy(y-x)-(y-x)}{xy(x-y)+(x-y)(x+y)}= \end{equation} \begin{equation} =\frac{(y-x)-(xy-1)}{(x-y)(xy+x-y)}= \end{equation} \begin{equation} =-\frac{xy-1}{xy+x-y}; \end{equation} \begin{equation} 4)\frac{a^{2}(b-c)-b^{2}(a-c)}{a(b-c)^{2}-b(a-c)^{2}}= \end{equation} \begin{equation} =\frac{a^{2}b-a^{2}c-}{ab^{2}-2abc+ac^{2}-} \end{equation} \begin{equation} \frac{b^{2}a+b^{2}c}{-ba^{2}+2abc-bc^{2}}= \end{equation} \begin{equation} =\frac{(a-b)\cdot ab-c(a-b)(a+b)}{(a-b)(-ab)+c^{2}(a-b)}= \end{equation} \begin{equation} =\frac{(a-b)(ab-ac-bc)}{(a-b)(c^{2}-ab)}= \end{equation} \begin{equation} =\frac{ab-ac-bc}{c^{2}-ab}; \end{equation} \begin{equation} 5)\frac{(a+1)^{3}+1}{a^{3}-1} \end{equation} \begin{equation} \frac{(a+1+1)((a+1)^{2})-}{(a-1)} \end{equation} \begin{equation} \frac{-(a+1)+1)}{(a^{2}-a+1)}= \end{equation} \begin{equation} =\frac{(a+2)(a^{2}+2a+}{(a-1)}= \end{equation} \begin{equation} \frac{+1-a-1+1)}{(a^{2}-a+1)}= \end{equation} \begin{equation} =\frac{(a+2)(a^{2}+a+1)}{(a-1)(a^{2}-a+1)}= \end{equation} \begin{equation} =\frac{a+2}{a-1}; \end{equation} \begin{equation} 6)\frac{(x-1)^{3}-1}{x^{3}+1} \end{equation} \begin{equation} \frac{((x-1)-1)((x-1)^{2}+}{(x+1)} \end{equation} \begin{equation} \frac{+(x-1)+1)}{(x^{2}-x+1)}= \end{equation} \begin{equation} =\frac{(x-2)(x^{2}+2x+}{(x+1)} \end{equation} \begin{equation} \frac{+1+x-1+1)}{(x^{2}-x+1)}= \end{equation} \begin{equation} =\frac{(x+2)(x^{2}-x+1)}{(x+1)(x^{2}-x+1)}= \end{equation} \begin{equation} =\frac{x+2}{x+1}. \end{equation}