a: ĐKXĐ: a<>1
\(M=\dfrac{a^2+a+1}{a^2+1}:\left(\dfrac{-1}{a-1}-\dfrac{2a}{\left(a-1\right)\left(a^2+1\right)}\right)\)
\(=\dfrac{a^2+a+1}{a^2+1}:\dfrac{-a^2-1-2a}{\left(a-1\right)\left(a^2+1\right)}\)
\(=\dfrac{a^2+a+1}{a^2+1}\cdot\dfrac{\left(a-1\right)\left(a^2+1\right)}{-\left(a+1\right)^2}=\dfrac{-\left(a-1\right)\left(a^2+a+1\right)}{\left(a+1\right)^2}=\dfrac{-\left(a^3-1\right)}{\left(a+1\right)^2}\)
c: M=7
=>-a^3+1=7(a^2+2a+1)
=>-a^3+1=7a^2+14a+7
=>a^3+7a^2+14a+6=0
=>a^3+3a^2+4a^2+12a+2a+6=0
=>(a+3)(a^2+4a+2)=0
=>a=-3 hoặc \(a=-2\pm\sqrt{2}\)
c: M>0
=>-(a^3-1)>0
=>a^3-1<0
=>a<1
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