Đáp án:
$5)D\\6)D\\7)D\\8)B$
Giải thích các bước giải:
$5)\\ \dfrac{5(y-x)^2}{5x^2-5xy}=\dfrac{x-y}{P}\\ \Rightarrow P=\dfrac{(5x^2-5xy)(x-y)}{5(y-x)^2}\\ =\dfrac{5x(x-y)(x-y)}{5(y-x)^2}\\ =\dfrac{5x(x-y)^2}{5(y-x)^2}\\ =x\\ 6)\\ \dfrac{x^3}{x^2+1}+\dfrac{x}{x^2+1}\\ =\dfrac{x^3+x}{x^2+1}\\ =\dfrac{x(x^2+1)}{x^2+1}\\=x\\ 7)\\ĐKXĐ: \left\{\begin{array}{l} x \ne 0\\x \ne -1 \\ x \ne -2 \\ x \ne -3 \\ x \ne -4 \\ x \ne -5 \\ x \ne -6\end{array} \right.\\ \dfrac{1}{x}.\dfrac{x}{x+1}.\dfrac{x+1}{x+2}.\dfrac{x+2}{x+3}.\dfrac{x+3}{x+4}.\dfrac{x+4}{x+5}.\dfrac{x+5}{x+6}=1\\ \Leftrightarrow \dfrac{1}{x+6}=1\\ \Leftrightarrow x+6=1\\ \Leftrightarrow x=-5(L)\\ 8)\\ \dfrac{x+2y}{x^3-8y^3}M=\dfrac{5x^2+10xy}{x^2+2xy+4y^2}\\ \Leftrightarrow \dfrac{x+2y}{x^3-8y^3}M=\dfrac{5x^2+10xy}{x^2+2xy+4y^2}\\ \Leftrightarrow \dfrac{x+2y}{x^3-(2y)^3}M=\dfrac{5x(x+2y)}{x^2+2xy+4y^2}\\ \Leftrightarrow \dfrac{x+2y}{(x-2y)(x^2+2xy+4y^2)}M=\dfrac{5x(x+2y)}{x^2+2xy+4y^2}\\ \Leftrightarrow \dfrac{1}{x-2y}M=5x\\ \Leftrightarrow M=5x(x-2y)$
