\(\Leftrightarrow\dfrac{6x^2-x-1}{x\left(x-1\right)\left(x+1\right)}=\dfrac{a\left(x-1\right)\left(x+1\right)+bx\left(x+1\right)+cx\left(x-1\right)}{x\left(x-1\right)\left(x+1\right)}\)
=>\(6x^2-x-1=a\left(x^2-1\right)+bx^2+bx+cx^2-cx\)
\(\Leftrightarrow6x^2-x-1=x^2\left(a+b+c\right)+x\left(b-c\right)-a\)
\(\Leftrightarrow\left\{{}\begin{matrix}a+b+c=6\\b-c=-1\\-a=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=1\\b-c=-1\\b+c=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=1\\b=2\\c=3\end{matrix}\right.\)
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