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Общая оценка

# Номер 51 гдз 8 класс алгебра Муравин Муравина

Номер 51

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