Question

Giải phương trình:  \(\frac{2}{x^2-x+1}=\frac{1}{x+1}+\frac{2x-1}{x^3+1}\)

Answer 1

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

\(\Rightarrow3x+1-x^2=2x-1\Rightarrow\left(x+1\right)\left(x-2\right)=0\Rightarrow x=2\)

Answer 2

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

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

ĐKXĐ : x\(\ne\)-1

MTC : (x+1)(x^2-x+1)

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

2x+2=x^2-x+1+2x-1

-x^2+2x-2x+x=-2+1-1

x-x^2=-2

x(1-x)=-2

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