:( eo ơi 

\(a,\dfrac{4\times5\times6}{12\times15\times9}=\dfrac{4\times5\times2\times3}{4\times3\times3\times5\times9}=\dfrac{2}{3\times9}=\dfrac{2}{27}\\ b,\dfrac{6\times8\times11}{33\times16}=\dfrac{2\times3\times4\times2\times11}{11\times3\times4\times4}=\dfrac{2\times2}{4}=\dfrac{4}{4}=1\)

\(a,P=\left(\dfrac{1}{x-2}-\dfrac{4}{x^2-4}\right):\dfrac{x+1}{2x+4}\\ =\left(\dfrac{1.\left(x+2\right)-4}{\left(x-2\right)\left(x+2\right)}\right)\times\dfrac{2\left(x+2\right)}{x+1}\\ =\dfrac{x+2-4}{\left(x-2\right)\left(x+2\right)}\times\dfrac{2\left(x+2\right)}{x+1}\\ =\dfrac{x-2}{\left(x-2\right)\left(x+2\right)}\times\dfrac{2\left(x+2\right)}{x+1}\\ \\ =\dfrac{2}{x+1}\)

\(b,\) Để \(P\) nguyên 

\(\Rightarrow x+1\inƯ\left(2\right)\\ Ư\left(2\right)=\left\{1;-1;2;-2\right\}\\ \Rightarrow\left\{{}\begin{matrix}x+1=1\\x+1=-1\\x+1=2\\x+1=-2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0\left(t/m\right)\\x=-2\left(kot/m\right)\\x=1\left(t/m\right)\\x=-3\left(t/m\right)\end{matrix}\right.\)

Vậy \(x=\left\{0;1;3\right\}\)

\(-5\dfrac{1}{7}=-\dfrac{5.7+1}{7}=-\dfrac{36}{7}\)

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