Đáp án`+`Giải thích các bước giải:

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\(\frac{4x^{2}-3x+17}{x^{3}-1}+\frac{2x-1}{x^{2}+x+1}+\frac{6}{1-x}\)

\(=\frac{4x^{2}-3x+17}{(x-1)(x^{2}+x+1)}+\frac{(2x-1)(x-1)}{(x-1)(x^{2}+x+1)}-\frac{6(x^{2}+x+1)}{(x-1)(x^{2}+x+1)}\)

\(=\frac{4x^{2}-3x+17+(2x^{2}-2x-x+1)-(6x^{2}+6x+6)}{(x-1)(x^{2}+x+1)}\)

\(=\frac{4x^{2}-3x+17+2x^{2}-3x+1-6x^{2}-6x-6}{(x-1)(x^{2}+x+1)}\)

\(=\frac{(4+2-6)x^{2}+(-3-3-6)x+(17+1-6)}{(x-1)(x^{2}+x+1)}\)

\(=\frac{-12x+12}{(x-1)(x^{2}+x+1)}\)

\(=\frac{-12(x-1)}{(x-1)(x^{2}+x+1)}\)

\(=\frac{-12}{x^{2}+x+1}\)